Find the following f(x)=x^2 - 4x - 12 a) f(a+2) b) f(a+h)

(A) f(a + 2) = a² - 16

substitute x = a + 2 into f(x)

f(a + 2) = (a + 2)² - 4(a + 2) - 12

           = a² + 4a + 4 - 4a - 8 - 12

           = a² - 16

(B ) f(a + h) = a² + 2ah + h² - 4a - 4h - 12

substitute x = a + h into f(x)

f(a + h) = a² + 2ah + h² - 4a - 4h - 12

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: