If `x ge 4, A^(2)=x^(2)+12x + 36`, and `B^(2)=4x^(2)-28x+49`, then `(A+B)^(2)=`

Options

A. `2x^(2)+5x+-42`
B. `3x^(2)-9x-1`
C. `4x^(2)-x+13`
D. `9x^(2)-6x+1`

Answer

D

Explanation

Since each polynomial is expressed in terms of the square of an expression, find the square root of each polynomial.
`A^(2)=x^(2)+12x+36=(x+6)^(2)`
`A=x+6`
`B^(2)=4x^(2)-28x+49=(2x-7)^(2)`
`B = 2x-7`
Now add the two binomial square roots.
`A+B=(x+6)+(2x-7)=3x-1`
`(A+B)^(2)=(3x-1)^(2)=9x^(2)-6x+1`