Perfect Square Trinomials are quadratics that is the result of squaring binomials. For instance, for the square of the sum:
[tex](a+b)^2[/tex]
We know that this equals:
[tex](a+b)(a+b)[/tex]
That is equivalent to the Perfect Square Trinomial:
[tex]a^2+2ab+b^2[/tex]
By knowing this, we can say that the correct answers are:
FIRST.
[tex](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!}[/tex]
SECOND.
[tex](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!}[/tex]
THIRD.
[tex](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!}[/tex]
Answer:
The correct option are 2,3 and 4.
Step-by-step explanation:
The form of perfect square trinomial are
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Simplify the all given expressions.
In option 1,
[tex](-x+9)(-x-9)=(-x)^2-(9)^2=x^2-9^2[/tex]
It is not a perfect square trinomial, therefore option 1 is incorrect.
In option 2,
[tex](xy+y)(xy+y)=(xy+y)^2[/tex]
It is a perfect square trinomial, therefore option 2 is correct.
In option 3,
[tex](2x-3)(-3+2x)=(2x-3)(2x-3)=(2x-3)^2[/tex]
It is a perfect square trinomial, therefore option 3 is correct.
In option 4,
[tex](4y^2+25)(25+4y^2)=(4y^2+25)(4y^2+25)=(4y^2+25)^2[/tex]
It is a perfect square trinomial, therefore option 4 is correct.
