2 8.1 expanding brackets - mrvahora · 2014. 10. 13. · 2 8.1 expanding brackets 119 hint remember...
TRANSCRIPT
1 Expand
a 2(x + 1) ................................... b 5(x –1) ...................................
c 3(p – q) ................................... d 4(2 – s) ...................................
2 Expand
a 3(2x + 1) ................................... b 2(5x – 3) ...................................
c 5(n2 – 3n) ................................... d 2(n2 – 3n) ...................................
3 Expand
a x(x – 1) ................................... b x(x + 4) ...................................
c y(3 – y) ................................... d p(p + 5) ...................................
4 Expand
a t(2t + 1) ................................... b y(3y – 2) ...................................
c x(4x + 3) ................................... d a(5 – 2a) ...................................
5 Expand
a −5(x – 1) ................................... b −3(x + 4) ...................................
c −2(3x + 4) ................................... d –x(x + 1) ...................................
6 Expand
a −4(y – 2) ................................... b −2(1 – x) ...................................
c −3m(m – 1) ................................... d −2x(x – 2) ...................................
7 Expand and simplify
a 2(x + 1) + 3x b 3(x + 2) + 4(x – 1)
.................................................................................................... ....................................................................................................
c x(y + 1) + y(x + 1) d x(x – 1) + 2x(x + 3)
.................................................................................................... ....................................................................................................
8 Expand and simplify
a 5(y + 2) – 2(y + 3) b y(y + 5) – y(y + 1)
.................................................................................................... ....................................................................................................
c 2y(y – 3) – 5(y – 1) d 3y(y – 5) – 2y(y – 2)
.................................................................................................... ....................................................................................................
�2 8.1 Expanding brackets
119
Hint Remember to multiply every term inside the bracket.
Hint Watch the signs outside and inside the bracket.
Guided practice worksheet
D
C
Questions are targeted at the grades indicated
1 Factorise
a 2x + 2 ................................. b 6x + 3 ................................. c 5x – 15 ................................. d 3 – 3x .................................
2 Factorise
a 10y + 25 ................................. b 7y – 14 ................................. c pq + qr ................................. d s2 – st .................................
3 Factorise fully
a 12x + 18 ............................................................... b 16x – 24 ...............................................................
c 3ab + 9a ............................................................... d 4x2 + 2x ...............................................................
4 Factorise fully
a 2y + 8y2 ............................................................... b p2q − pq2 ...............................................................
c 27a2 – 18a ............................................................... d 30x2 + 50xy ...............................................................
5 Factorise
a x(x + 1) + x(x + 2) b (x – 1)2 + (x – 1)
.................................................................................................... ....................................................................................................
c 2(x + 3) + (x + 3)2
....................................................................................................
6 Factorise fully
a 3x(x + 1) + 6x(x + 2) b 5(x – 2)2 – 10(x – 2)
.................................................................................................... ....................................................................................................
c 4(3x + 1)2 – 2(3x + 1)
....................................................................................................
�2 8.2 Factorising by taking out common factors
121
Guided practice worksheet
D
C
B
Questions are targeted at the grades indicated
�2 8.3 Expanding the product of two brackets
123A
Expand and simplify the following brackets
1 (x + 4) (x + 5)
..................................................................................
3 (x + 3) (x + 6)
..................................................................................
5 (x + 3) (x – 2)
..................................................................................
7 (x – 1) (x + 3)
..................................................................................
9 (x – 3) (x – 4)
..................................................................................
1 1 (x + 4)2
..................................................................................
2 (x + 2) (x + 8)
..................................................................................
4 (x + 1) (x + 9)
..................................................................................
6 (x + 5) (x – 5)
..................................................................................
8 (x – 4) (x + 2)
..................................................................................
1 0 (x – 5) (x – 6)
..................................................................................
1 2 (x – 6)2
..................................................................................
Hint Multiply every term inside the bracket by every term outside the bracket.
Guided practice worksheet
B
Questions are targeted at the grades indicated
�2 8.3 Expanding the product of two brackets
123B
1 3 (2x + 1) (x + 2)
..................................................................................
1 5 (x – 1) (2x + 1)
..................................................................................
1 7 (x – 3) (3x – 1)
..................................................................................
1 9 (2x – 5)2
..................................................................................
1 4 (3x + 1) (2x + 3)
..................................................................................
1 6 (4x + 5) (x – 2)
..................................................................................
1 8 (2x + 5)2
..................................................................................
2 0 (3x + y)2
..................................................................................
Guided practice worksheet
A
�2 8.4 Factorising quadratic expressions
125A
1 a Write down a pair of numbers whose product is +2 and whose sum is +3.
..................................................................................................
b Factorise x2 + 3x + 2. ..................................................................................................
2 a Write down a pair of numbers whose product is −3 and whose sum is +2.
..................................................................................................
b Factorise x2 + 2x – 3. ..................................................................................................
3 a Write down a pair of numbers whose product is +7 and whose sum is −8.
..................................................................................................
b Factorise x2 – 8x + 7 ..................................................................................................
4 Factorise
a x2 + 6x + 5 b x2 + 10x + 21
...................................................................................................... ......................................................................................................
5 Factorise
a x2 + 5x – 24 b x2 – x – 20
...................................................................................................... ......................................................................................................
6 Factorise
a x2 – 9x + 8 b x2 – 18x + 81
...................................................................................................... ......................................................................................................
7 Use the difference of two squares to factorise
a x2 – 16 b x2 – 121 c 25 − x2
............................................ ............................................ ............................................
Guided practice worksheet
B
A2 − B2 = (A + B) (A –B)
Questions are targeted at the grades indicated
A
�2 8.4 Factorising quadratic expressions
125B
Guided practice worksheet
8 Complete the following
a 2x2 +5x + 2 = (2x + 1) (.............................................)
b 6x2 + 5x – 4 = (3x + 4) (.............................................)
c 4x2 – 9x + 2 = (4x – 1) (.............................................)
9 Factorise 5x2 + 31x + 6
..................................................................................................
1 0 Factorise 6x2 – 5x – 25
..................................................................................................
A