Question

Which products result in a perfect square trinomial? Check all that apply. (–x + 9)(–x – 9) (xy + x)(xy + x) (2x – 3)(–3 + 2x) (16 – x2)(x2 – 16) (4y2 + 25)(25 + 4y2)

Answer 1

Perfect Square Trinomials are quadratics that is the result of squaring binomials. For instance, for the square of the sum:

`(a+b)^2`

We know that this equals:

`(a+b)(a+b)`

That is equivalent to the Perfect Square Trinomial:

`a^2+2ab+b^2`

By knowing this, we can say that the correct answers are:

FIRST.

`(xy + x)(xy + x) \\ \\ =(xy+x)^2 \\ \\ = (xy)^2+2(xy)(x)+x^2 \\ \\ \\ = \boxed{x^2y^2+2x^2y+y^2, \ is \ a \ Perfect \ Square \ Trinomial!}`

SECOND.

`(2x-3)(-3 + 2x) \\ \\ (2x-3)(2x-3) \\ \\ =(2x-3)^2 \\ \\ = (2x)^2-2(2x)(3)+3^2 \\ \\ \\ = \boxed{4x^2-12x+9, \ is \ a \ Perfect \ Square \ Trinomial!}`

THIRD.

`(4y^2+25)(25+4y^2) \\ \\ (4y^2+25)(4y^2+25) \\ \\ =(4y^2+25)^2 \\ \\ = (4y^2)^2+2(4y^2)(25)+25^2 \\ \\ \\ = \boxed{16y^4+200y^2+625, \ is \ a \ Perfect \ Square \ Trinomial!}`

Answer 2

The correct option are 2,3 and 4.

Explanation:

The form of perfect square trinomial are

`(a+b)^2=a^2+2ab+b^2`

`(a-b)^2=a^2-2ab+b^2`

Simplify the all given expressions.

In option 1,

`(-x+9)(-x-9)=(-x)^2-(9)^2=x^2-9^2`

It is not a perfect square trinomial, therefore option 1 is incorrect.

In option 2,

`(xy+y)(xy+y)=(xy+y)^2`

It is a perfect square trinomial, therefore option 2 is correct.

In option 3,

`(2x-3)(-3+2x)=(2x-3)(2x-3)=(2x-3)^2`

It is a perfect square trinomial, therefore option 3 is correct.

In option 4,

`(4y^2+25)(25+4y^2)=(4y^2+25)(4y^2+25)=(4y^2+25)^2`

It is a perfect square trinomial, therefore option 4 is correct.