Question

Which of the following is the square of a binomial?

Answer 1

ANSWER

D.

$16 {x}^{2} + 24xy + 9 {y}^{2}$

EXPLANATION

We want to find the expression which is a square of a binomial.

In other words, we want to identify the expression which is a perfect square trinomial.

$16 {x}^{2} + 24xy + 9 {y}^{2}$

This expression can be rewritten as,

${(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2}$

This is a perfect square trinomial that can be factored as:

${(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} = (4x + 3y) ^{2}$

This is the square of a binomial.

The correct answer is D

Answer 2

Hello!

The answer is:

D) $16x^{2} +24xy+9y^{2}$

Why?

We are looking for an expression that satisfies the perfect square trinomial form, which can be defined by the following notable product:

$(a+b)^{2}=a^{2}+2ab+b^{2}$

From the given options, we can see that the only option that matches with the perfect square trinomial form is:

$16x^{2} +24xy+9y^{2}$

We can rewrite the expression by the following way:

$(4x+3y)^{2}$

If we square the binomial, we will have the perfect square binomial expression given from the options.

So, squaring, we have:

$(4x+3y)^{2}=(4x)^{2}+2*(4x*3y)+(3y)^{2}\\\\(4x+3y)^{2}=16x^{2} +24xy+9y^{2}$

Hence, the answer is:

D) $16x^{2} +24xy+9y^{2}$

Have a nice day!