topic 2 multiplying polynomials - part 1
TRANSCRIPT
Multiplying Polynomials
Module 9 - Topic 2Part 1
Multiply a Polynomial by a Monomial
Multiply each term inside the parenthesis by the monomial outside the parenthesis.
The number of terms inside the parenthesis will be the same as after multiplying.
3x2 2x2 ! 7x + 5( )
Multiply a Polynomial by a Monomial
Multiply each term inside the parenthesis by the monomial outside the parenthesis.
The number of terms inside the parenthesis will be the same as after multiplying.
3x2 2x2 ! 7x + 5( )3x2 2x2( ) + 3x2 !7x( ) + 3x2 5( )
Multiply a Polynomial by a Monomial
Multiply each term inside the parenthesis by the monomial outside the parenthesis.
The number of terms inside the parenthesis will be the same as after multiplying.
3x2 2x2 ! 7x + 5( )3x2 2x2( ) + 3x2 !7x( ) + 3x2 5( )
3x2 2x2 ! 7x + 5( )
Multiply a Polynomial by a Monomial
Multiply each term inside the parenthesis by the monomial outside the parenthesis.
The number of terms inside the parenthesis will be the same as after multiplying.
3x2 2x2 ! 7x + 5( )3x2 2x2( ) + 3x2 !7x( ) + 3x2 5( )
6x4 ! 21x3 +15x23x2 2x2 ! 7x + 5( )
Multiply a Polynomial by a Monomial
Review this Cool Math site to learn about multiplying a polynomial by a monomial.
Do the Try It and Your Turn problems in your notebook and check your answers on the next slides.
Try It - Page 1Multiply: 6x4 2x2 + 3( )
Try It - Page 1Multiply: 6x4 2x2 + 3( )
Distribute the monomial.
Try It - Page 1Multiply: 6x4 2x2 + 3( )
6x4 !2x2 + 6x4 ! 3Distribute the monomial.
Try It - Page 1Multiply: 6x4 2x2 + 3( )
6x4 !2x2 + 6x4 ! 3Distribute the monomial.
Multiply each term.
Try It - Page 1Multiply: 6x4 2x2 + 3( )
6x4 !2x2 + 6x4 ! 3
12x6 +18x4
Distribute the monomial.
Multiply each term.
Try It - Page 1Multiply: 6x4 2x2 + 3( )
6x4 !2x2 + 6x4 ! 3
12x6 +18x4
Distribute the monomial.
Multiply each term.
Verify your answer has same number of terms as inside original ( ). Both have 2 terms.
Your Turn - Page 2multiply:
Your Turn - Page 2multiply: 10x3 2x5 +1! 3x2 + x( )
Your Turn - Page 2multiply: 10x3 2x5 +1! 3x2 + x( )
Distribute the monomial.
Your Turn - Page 2multiply: 10x3 2x5 +1! 3x2 + x( )
Distribute the monomial.
10x3 2x5( ) +10x3 1( ) +10x3 !3x2( ) +10x3 x( )
Your Turn - Page 2multiply: 10x3 2x5 +1! 3x2 + x( )
Multiply each term.
10x3 2x5( ) +10x3 1( ) +10x3 !3x2( ) +10x3 x( )
Your Turn - Page 2multiply: 10x3 2x5 +1! 3x2 + x( )
20x8 +10x3 ! 30x5 +10x4Multiply each term.
10x3 2x5( ) +10x3 1( ) +10x3 !3x2( ) +10x3 x( )
Your Turn - Page 2multiply: 10x3 2x5 +1! 3x2 + x( )
20x8 +10x3 ! 30x5 +10x4
10x3 2x5( ) +10x3 1( ) +10x3 !3x2( ) +10x3 x( )
Put in descending order and verify number of terms.
(Both have 4 terms.)
Your Turn - Page 2multiply: 10x3 2x5 +1! 3x2 + x( )
20x8 +10x3 ! 30x5 +10x4
10x3 2x5( ) +10x3 1( ) +10x3 !3x2( ) +10x3 x( )
Put in descending order and verify number of terms.
(Both have 4 terms.) 20x8 ! 30x5 +10x4 +10x3
Try It - Page 2Multiply: 4x2w5 w ! x2 + 6xw2 !1+ 3x4w8( )
Try It - Page 2Multiply: 4x2w5 w ! x2 + 6xw2 !1+ 3x4w8( )
Distribute the monomial.
Try It - Page 2Multiply: 4x2w5 w ! x2 + 6xw2 !1+ 3x4w8( )
Distribute the monomial.
4x2w5 w( ) + 4x2w5 !x2( ) + 4x2w5 6xw2( ) + 4x2w5 !1( ) + 4x2w5 3x4w8( )
Try It - Page 2Multiply: 4x2w5 w ! x2 + 6xw2 !1+ 3x4w8( )
Multiply each term.
4x2w5 w( ) + 4x2w5 !x2( ) + 4x2w5 6xw2( ) + 4x2w5 !1( ) + 4x2w5 3x4w8( )
Try It - Page 2Multiply: 4x2w5 w ! x2 + 6xw2 !1+ 3x4w8( )
Multiply each term.
4x2w5 w( ) + 4x2w5 !x2( ) + 4x2w5 6xw2( ) + 4x2w5 !1( ) + 4x2w5 3x4w8( )
4x2w6 ! 4x4w5 + 24x3w7 ! 4x2w5 +12x6w13
Verify answer has 5 terms like original parenthesis.
Multiply:
Try this one...3x 2x2 ! 5x + 7( )
Multiply:
Try this one...3x 2x2 ! 5x + 7( )
Distribute the monomial.
Multiply:
Try this one...3x 2x2 ! 5x + 7( )
Distribute the monomial.
3x 2x2( ) + 3x ! "5x( ) + 3x 7( )
Multiply:
Try this one...3x 2x2 ! 5x + 7( )
3x 2x2( ) + 3x ! "5x( ) + 3x 7( )Multiply each term.
Multiply:
Try this one...3x 2x2 ! 5x + 7( )
3x 2x2( ) + 3x ! "5x( ) + 3x 7( )Multiply each term.
6x3 !15x2 + 21x
Multiply:
Try this one...!2a2b2 a3 + 3a22b3 ! 4b5( )
Multiply:
Try this one...!2a2b2 a3 + 3a22b3 ! 4b5( )
Distribute the monomial.
Multiply:
Try this one...!2a2b2 a3 + 3a22b3 ! 4b5( )
Distribute the monomial.
!2a2b2( ) a3( ) + !2a2b2( ) 3a22b3( ) + !2a2b2( ) !4b5( )
Multiply:
Try this one...!2a2b2 a3 + 3a22b3 ! 4b5( )
Multiply each term.
!2a2b2( ) a3( ) + !2a2b2( ) 3a22b3( ) + !2a2b2( ) !4b5( )
Multiply:
Try this one...!2a2b2 a3 + 3a22b3 ! 4b5( )
Multiply each term.
!2a2b2( ) a3( ) + !2a2b2( ) 3a22b3( ) + !2a2b2( ) !4b5( )
!2a5b2 ! 6a4b5 + 8a2b7
Great job working all those problems!
Proceed to Part 2.