Question

1. $\frac{b^2 - 2b + 1}{b^2} = \frac{b^2 - 2b + 1}{b^2}$
2. $(x - 2)(x + 3) = x^2 + x - 6$
3. $(2x - 1)(4x + 3) = 8x^2 + 2x - 3$
4. $(x - \frac{1}{4})(x + \frac{1}{2}) = x^2 + \frac{1}{4}x - \frac{1}{8}$

find the square for each equation.

1. $(x - 2)^2 = $
2. $(a + b)^2 = $
3. $(x^3 - x)^2 = $
4. $(x + 3)^2 = $

Explanation:

Step1: Apply square of binomial formula

Use $(m-n)^2=m^2-2mn+n^2$

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

Step2: Apply square of binomial formula

Use $(m+n)^2=m^2+2mn+n^2$

$$\begin{align*} (a+b)^2&=a^2+2(a)(b)+b^2\\ &=a^2+2ab+b^2 \end{align*}$$

Step3: Apply square of polynomial formula

Use $(m-n)^2=m^2-2mn+n^2$ where $m=x^3, n=x$

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

Step4: Apply square of binomial formula

Use $(m+n)^2=m^2+2mn+n^2$

$$\begin{align*} (x+3)^2&=x^2+2(x)(3)+3^2\\ &=x^2+6x+9 \end{align*}$$

Answer:

1. $x^2-4x+4$
2. $a^2+2ab+b^2$
3. $x^6-2x^4+x^2$
4. $x^2+6x+9$