Slideshow 4Mr Richard Sasaki

Room 307

Multiplying Polynomials by a Number

Objectives

Recall how a ‘-’ affects terms within brackets

Learn how a number changes terms within brackets

Multiplying polynomials by a number

How “-” affects a polynomial

−(3 𝑥+7 𝑦 – 𝑧 /2)=−3 𝑥−7 𝑦+𝑧 /2

As you are well aware now, the minus symbol swaps each symbol around for each term in the polynomial.

How a number affects a polynomial

As with the minus symbol, any number will affect each term in the polynomial by multiplication.

2(𝑥+𝑦 )=2 𝑥+2 𝑦Each of the terms above has been multiplied by two.

How a number affects a polynomial

Each of the coefficients in the polynomial will be multiplied by the number outside the bracket.

4(3𝑥−2 𝑦 )=12𝑥−8 𝑦So here we did 4 x 3 = 12 and -2 x 4 = -8.

How a number affects a polynomial

ExampleSimplify the expression below.

−3 (5 𝑥−4 𝑦−7)=−15 𝑥+12 𝑦+21

As you can see, the minus symbol swaps the symbol in front of each term as usual.

Adding and Subtracting Polynomials with coefficients in front of brackets

After we expand brackets for a polynomial, we can add or subtract this polynomial to another.

2(𝑥+𝑦 )+2 (𝑦+𝑧)=[2𝑥+2 𝑦 ]+[2 𝑦+2𝑧 ]=2 𝑥+2 𝑦+2 𝑦+2 𝑧=2 𝑥+4 𝑦+2 𝑧

How a number affects a polynomial

ExampleSimplify the expression below.

4(2𝑥+3 𝑦 )−3 (3 𝑦−𝑧−4 )=[8 𝑥+12 𝑦 ]−[9 𝑦−3 𝑧−12]=8 𝑥+12 𝑦−9 𝑦+3 𝑧+12=8 𝑥+3 𝑦+3 𝑧+12

Try the worksheets, good luck!

Answers - Easy

𝟑 𝒙+𝟑𝒚𝟓𝒂 –𝟓𝒃−𝟐 𝒙−𝟐 𝒚𝟏𝟎𝒙+𝟏𝟎𝒚 −𝟏𝟎 𝒛−𝟓𝒂+𝟓𝒃–𝟓𝒄𝟐𝒂+𝟐𝒃𝟐 𝒙+𝟒 𝒚

𝟒 (𝒙+𝒚 )𝟓𝒂+𝟓𝒃

𝟏𝟐𝒙+𝟖 𝒚−𝒚

−𝟐 𝒙 –𝟒 𝒚

Answers - Medium

𝟏𝟎𝒂+𝟏𝟓𝒃−𝟐 𝒙+𝟐 𝒚−𝟓 𝒙 –𝟓 𝒚+𝟓 𝒛−𝟒𝒂+𝟑𝒃−𝟓𝒄𝟔𝒂+𝟐𝟏𝒃−𝟏𝟓−𝟔 𝒙+𝟐𝟕𝒚−𝟔 𝒙+𝟖 𝒚

(𝟐𝟕𝒙+𝟐𝟒) – (𝟏𝟐𝒙 –𝟔)−𝟏𝟎𝒙 𝟐+𝟏𝟏𝒙𝟒 (𝟒 𝒙 –𝟑)+𝟓(𝟕 𝒚 –𝟑)𝟖𝒂+𝟐𝒃−𝟏𝟒

(−𝟏𝟐 𝒙+𝟖 𝒚 )+(𝟗𝒙 –𝟐 𝒚+𝒛 )

Answers - Hard

𝒙 –𝟒 𝒚−𝟒+𝟒 𝒙𝟐+𝟏𝟐𝒙𝟓/𝟐 𝒙−𝟑/𝟐 𝒚𝟏𝟐𝒂 –𝟏𝟐𝒃+𝟏𝟐𝒄𝟐𝟒𝒂 –𝟏𝟐𝒃

𝟒𝒂−𝟔𝒃

𝟐𝟎𝒙+𝟏𝟗𝒚 –𝟐𝟏 𝒛−𝟗

−𝟑𝟔𝒙+𝟗𝟕