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

2. 13.05 Multiplying Binomials

3. 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.

4. ( a + b )( c + d ) = a ( c + d ) + b ( c + d )
( x )( x )
x ( x ) ( x )
x x + 3x
x x
( x – 5 )( x )
x ( x ) – 5 ( x )
x x – 5x – 40
x x – 40

5. ( a + b )( c + d ) = a ( c + d ) + b ( c + d )
( 2x )( 3x )
2x ( 3x ) ( 3x )
6x x x
6x x
( x – 4 )( 8x – 1 )
x ( 8x – 1 ) – 4 ( 8x – 1 )
8x2 – 1x – 32x + 4
8x2 – 33x + 4

6. Try This:
( a + b )( c + d ) = a ( c + d ) + b ( c + d )
(x )(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