Question

1. write the expression equivalent to

$(5x + 4)^2$

1. write the expression equivalent to

$(7x + 2)^2$

1. write the expression equivalent to

$(-5b + 6)(b^2 + 8b - 2)$

1. write the expression equivalent to

$(2x + 10)(x^2 + 3x - 4)$

Explanation:

Step1: Apply square of sum formula

For $(5x + 4)^2$, use $(a+b)^2=a^2+2ab+b^2$:

$$\begin{align*} (5x)^2 + 2(5x)(4) + 4^2 &= 25x^2 + 40x + 16 \end{align*}$$

Step2: Apply square of sum formula

For $(7x + 2)^2$, use $(a+b)^2=a^2+2ab+b^2$:

$$\begin{align*} (7x)^2 + 2(7x)(2) + 2^2 &= 49x^2 + 28x + 4 \end{align*}$$

Step3: Distribute each term

For $(-5b + 6)(b^2 + 8b - 2)$, distribute $-5b$ and $6$:

$$\begin{align*} -5b(b^2 + 8b - 2) + 6(b^2 + 8b - 2) &= -5b^3 -40b^2 +10b +6b^2 +48b -12 \end{align*}$$

Combine like terms:
$-5b^3 + (-40b^2+6b^2) + (10b+48b) -12 = -5b^3 -34b^2 +58b -12$

Step4: Distribute each term

For $(2x + 10)(x^2 + 3x - 4)$, distribute $2x$ and $10$:

$$\begin{align*} 2x(x^2 + 3x - 4) + 10(x^2 + 3x - 4) &= 2x^3 +6x^2 -8x +10x^2 +30x -40 \end{align*}$$

Combine like terms:
$2x^3 + (6x^2+10x^2) + (-8x+30x) -40 = 2x^3 +16x^2 +22x -40$

Answer:

1. $25x^2 + 40x + 16$
2. $49x^2 + 28x + 4$
3. $-5b^3 - 34b^2 + 58b - 12$
4. $2x^3 + 16x^2 + 22x - 40$