Question

Which of the following is the square of a binomial?


`A)c^2-2cd-d^2\\\\B)a^2+b^2\\\\C)4m^2-6mn+9n^2\\ \\D)16x^2+24xy+9y^2`

Answer 1

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!

Answer 2

D.

`16 {x}^(2) + 24xy + 9 {y}^(2)`

Step-by-step 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 * 3)xy + {(3y)}^(2)`

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

`{(4x)}^(2) + 2(4 * 3)xy + {(3y)}^(2) = (4x + 3y) ^(2)`

This is the square of a binomial.

The correct answer is D