Question

select all the expressions that are perfect squares.
a ((x + 5)(x + 5)

b ((-9 + c)(c - 9)

c ((y - 10)(10 - y)

d ((a + 3)(3 + a)

e ((2x - 1)(2x + 1)

f ((4 - 3x)(3 - 4x)

g ((a + b)(b + a)

Explanation:

Step1: Identify perfect square form

A perfect square is of the form $(m)^2 = m \times m$, where $m$ is an algebraic expression.

Step2: Analyze Option A

Rewrite as identical factors:
$(x+5)(x+5)=(x+5)^2$

Step3: Analyze Option B

Rearrange terms:
$(-9+c)(c-9)=(c-9)(c-9)=(c-9)^2$

Step4: Analyze Option C

Factor out -1:
$(y-10)(10-y)=-(y-10)(y-10)=-(y-10)^2$, which is a negative of a perfect square, not a perfect square itself.

Step5: Analyze Option D

Rearrange terms:
$(a+3)(3+a)=(a+3)(a+3)=(a+3)^2$

Step6: Analyze Option E

This is a difference of squares:
$(2x-1)(2x+1)=(2x)^2-1^2$, not a perfect square.

Step7: Analyze Option F

Multiply terms:
$(4-3x)(3-4x)=12-16x-9x+12x^2=12x^2-25x+12$, which is not a perfect square trinomial.

Step8: Analyze Option G

Rearrange terms:
$(a+b)(b+a)=(a+b)(a+b)=(a+b)^2$

Answer:

A. $(x + 5)(x + 5)$
B. $(-9 + c)(c - 9)$
D. $(a + 3)(3 + a)$
G. $(a + b)(b + a)$