Mathematics, 21.11.2019 22:31 xmanavongrove55

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)

Answers: 3

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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 from: Angelofpink2590

The correct option are 2,3 and 4.

Step-by-step 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.

Answer from: Quest

Did u want to find the value of x?

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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Which products result in a perfect square trinomial? check all that apply. (–x + 9)(–x – 9) (xy + x...

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