1. Using Laws Of Exponents Objective: To use the laws of exponents to multiply polynomials

2. Laws Of Exponents a m a n = a m+n (ab) m = a m b m (a m ) n = a mn

3. Examples of how they work 1.a m a n = a m+n a 3 a 4 = (a a a)(a a a a) = a 7 a 3 a 4 = a 3 + 4 = a 7 2.(ab) 3 = (ab)(ab)(ab) = (a a a)(b b b) = a 3 b 3 3.(a 2 ) 3 = (a 2 )(a 2 )(a 2 ) = a a a a a a = a 6 4.(a 2 ) 3 = a 2 3 = a 6

4. Try These 1.(2x 3 y 2 )(-5xy 3 ) 2.(a 2 b 3 ) 4 3.(-2x 3 ) 2 4.a (a 4 ) 3 a 4 1.-10x 4 y 5 solution solution 2.a 8 b 12 solution solution 3.4x 6 solution solution 4.a 17 solution solution More examplesexamples

5. (2x 3 y 2 )(-5xy 3 ) (2 -5)(x 3 x)(y 2 y 3 ) (2 -5)(x 3+1 )(y 2+3 ) -10x 4 y 5 Back to Try These!

6. (a 2 b 3 ) 4 (a 2 ) 4 (b 3 ) 4 (a 24 )(b 34 ) a 8 b 12 Back to Try These!

7. (-2x 3 ) 2 (-2) 2 (x 3 ) 2 (-2) 2 (x 32 ) 4x 6 Back to Try These!

8. a (a 4 ) 3 a 4 a (a 12 ) a 4 a 1 + 12 + 4 = a 17 Back to Try These!

9. Try A Few More 1.3x 2 (4x 2 + 2x + 1) 2.x a+b (x a – b + x a+1 ) 12x 4 + 6x 3 + 3x 2 solution x 2a + x 2a + b + 1 solution End Show

10. 3x 2 (4x 2 + 2x + 1) (3x 2 )4x 2 + (3x 2 )2x + (3x 2 )1 12x 4 + 6x 3 + 3x 2 Try a Few More

11. x a+b (x a – b + x a+1 ) (x a+b )x a – b + (x a+b ) x a+1 x a + b + a – b + x a + b + a + 1 x 2a + x 2a + b + 1 you cannot add these together they are not like terms