Question

Which products result in a perfect square trinomial? Select three options.

(negative x + 9)(negative x minus 9)
(x y + x)(x y + x)
(2 x minus 3)(negative 3 + 2 x)
(16 minus x squared)(x squared minus 16)
(4 y squared + 25)(25 + 4 y squared)

Answer 1

Answer:

Second option: $(xy+x)(xy+x)$

Third option: $(2x-3)(-3+2x)$

Fifth option: $(4y^2+25)(25+4y^2)$

Step-by-step explanation:

By definition, a perfect square trinomial can be obtained by squaring binomials.

Then:

$(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2\\\\(a-b)^2=(a-b)(a-b)=a^2-2ab+b^2$

Knowing this, to obtain a perfect square trinomial, the binomials that you multiply must be equals.

Therefore, the products result in a perfect square trinomial are:

$(xy+x)(xy+x)=(xy+x)^2=(xy)^2+2(xy)(x)+x^2=x^2y^2+2x^2y+x^2$

$(2x-3)(-3+2x)=(2x-3)^2=(2x)^2-2(2x)(3)+3^2=4x^2-12x+9$

$(4y^2+25)(25+4y^2)=(4y^2+25)^2=(4y^2)^2+2(4y^2)(25)+25^2=16y^4+200y^2+625$

Answer 2

A perfect square trinomial is given by options B), C), and E) and this can be determined by using the arithmetic operations.

A perfect square trinomial is given by:

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

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

Therefore, from the given option the perfect trinomial is given by:

A) $(-x+9)(-x-9)=x^2-9^2=x^2 - 81$

B) $(xy+x)(xy+x) = (xy)^2+x^2+2x^2y$

C) $(2x-3)(-3+2x)=-6x+4x^2+9-6x=4x^2-12x+9$

D) $(16-x^2)(x^2-16) = 16x^2-256-x^4+16x^2$

E) $(4y^2+25)(25+4y^2)= 16y^4+200y^2+625$

Therefore, the correct option is B), C), and E).

For more information, refer to the link given below:

https://brainly.com/question/2096984