Question

factor.

1. $4x^{2}+12x+9$
2. $x^{2}-10xy+25y^{2}$
3. $8x^{2}+8x+2$

Explanation:

Problem 1: $4x^2 + 12x + 9$

Step1: Identify perfect square terms

$4x^2=(2x)^2$, $9=3^2$

Step2: Verify middle term

$2*(2x)*3=12x$, matches the middle term

Step3: Apply perfect square formula

$(a+b)^2=a^2+2ab+b^2$, so $a=2x, b=3$
Expression: $(2x+3)^2$

Problem 2: $x^2 - 10xy + 25y^2$

Step1: Identify perfect square terms

$x^2=(x)^2$, $25y^2=(5y)^2$

Step2: Verify middle term

$2*(x)*(5y)=10xy$, matches the middle term (with negative sign)

Step3: Apply perfect square formula

$(a-b)^2=a^2-2ab+b^2$, so $a=x, b=5y$
Expression: $(x-5y)^2$

Problem 3: $8x^2 + 8x + 2$

Step1: Factor out GCF first

GCF of 8,8,2 is 2
Expression: $2(4x^2+4x+1)$

Step2: Identify perfect square terms

$4x^2=(2x)^2$, $1=1^2$

Step3: Verify middle term

$2*(2x)*1=4x$, matches the middle term

Step4: Apply perfect square formula

$(a+b)^2=a^2+2ab+b^2$, so $a=2x, b=1$
Expression: $2(2x+1)^2$

Answer:

1. $(2x+3)^2$
2. $(x-5y)^2$
3. $2(2x+1)^2$