= 12x4 + 20x2 = 6x3 + 7x2 – x = – 16x5 + 72x4 = 24x3 – 6x2 + 48x Simplify the following expressions. 1) 4x2( 3x2 + 5 ) = 12x4 + 20x2 = 6x3 + 7x2 – x 2) x( 6x2 + 7x – 1 ) = – 16x5 + 72x4 3) – 8x3( 2x2 – 9x ) 4) 6x( 4x2 – x + 8 ) = 24x3 – 6x2 + 48x = 10x4 + 2x3 – 12x2 5) 2x2( 5x2 + x – 6 )

13.05 Multiplying Binomials

Remember that a binomial has 2 terms. x + 6 4x – 7 To multiply binomials, multiply each term in the 1st binomial by the entire 2nd binomial. ( a + b )( c + d ) = a ( c + d ) + b ( c + d ) = ac + ad + bc + bd Combine any like terms and write the polynomial in descending order.

( a + b )( c + d ) = a ( c + d ) + b ( c + d ) ( x + 3 )( x + 9 ) x ( x + 9 ) + 3 ( x + 9 ) x2 + 9x + 3x + 27 x2 + 12x + 27 ( x – 5 )( x + 8 ) x ( x + 8 ) – 5 ( x + 8 ) x2 + 8x – 5x – 40 x2 + 3x – 40

( a + b )( c + d ) = a ( c + d ) + b ( c + d ) ( 2x + 5 )( 3x + 7 ) 2x ( 3x + 7 ) + 5 ( 3x + 7 ) 6x2 + 14x + 15x + 35 6x2 + 29x + 35 ( x – 4 )( 8x – 1 ) x ( 8x – 1 ) – 4 ( 8x – 1 ) 8x2 – 1x – 32x + 4 8x2 – 33x + 4

Try This: ( a + b )( c + d ) = a ( c + d ) + b ( c + d ) (x + 3 )(x – 5 ) x ( x – 5 ) + 3 ( x – 5 ) x2 – 5x + 3x – 15 x2 – 2x – 15 ( 2x – 1 )( 5x – 2 ) 2x ( 5x – 2 ) – 1 ( 5x – 2 ) 10x2 – 4x – 5x + 2 10x2 – 9x + 2