Question

1. the expression $4x^2 + 4x + 1$ can be factored as

$(4x + 2)(2x + 1)$
$(2x + 1)^2$
$(x + 1)(2x + 1)$
$(x + 4)^2$

Explanation:

Step1: Recall perfect square formula

The perfect square trinomial formula is $(a+b)^2 = a^2 + 2ab + b^2$.

Step2: Match to given expression

For $4x^2 + 4x + 1$, identify $a=2x$ (since $(2x)^2=4x^2$) and $b=1$ (since $1^2=1$). Check the middle term: $2ab=2*(2x)*1=4x$, which matches.

Step3: Verify other options

• $(4x+2)(2x+1)=8x^2+8x+2

eq 4x^2+4x+1$

• $(x+1)(2x+1)=2x^2+3x+1

eq 4x^2+4x+1$

• $(x+4)^2=x^2+8x+16

eq 4x^2+4x+1$

Answer:

$\boldsymbol{(2x+1)^2}$