Question

Simplify: $4x^2{y}^2(2k{x}^2+x^3-1)=64x^4{y}^2$ and find the value of $k$.

• A. $8$
• B. $12$
• C. $6$
• D. $64$

Answer 1

The correct option is A $8$

$4x^2{y}^2(2k{x}^2+x^3-1)=64x^4{y}^2$
First, multiply each term of the monomial by the first term of the polynomial.
$4x^2{y}^2.2k{x}^2+4x^2{y}^2.x^3-4x^2{y}^2.1=64x^4{y}^2$
$8k{x}^4{y}^2+4x^5{y}^2-4x^2{y}^2=64x^4{y}^2$
The coefficients on each pair of like terms must be equal.
So, $8k=64$
$k=\frac{64}{8}$
$k=8$.