Square of Difference: More than one factorization

Question 1

$$ (x+3)^2=(x-3)^2 $$

Question 2

$$ (x-1)^2=x^2 $$

Question 3

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

Question 4

$$ $$ x^2+(x-2)^2=2(x+1)^2 $$

Question 5

$$ (x+3)^2=(x-3)^2 $$

Examples with solutions for Square of Difference: More than one factorization

Exercise #1

$(x+3)^2=(x-3)^2$

Video Solution

Step-by-Step Solution

Let's examine the given equation:

$(x+3)^2=(x-3)^2$ First, let's simplify the equation, for this we'll use the perfect square formula for a binomial squared:

$(a\pm b)^2=a^2\pm2ab+b^2$ ,

We'll start by opening the parentheses on both sides simultaneously using the perfect square formula mentioned, then we'll move terms and combine like terms, and in the final step we'll solve the simplified equation we get:

$(x+3)^2=(x-3)^2 \\ \downarrow\\ x^2+2\cdot x\cdot3+3^2= x^2-2\cdot x\cdot3+3^2 \\ x^2+6x+9= x^2-6x+9 \\ x^2+6x+9- x^2+6x-9 =0\\ 12x=0\hspace{6pt}\text{/}:12\\ \boxed{x=0}$ Therefore, the correct answer is answer A.

Answer

$x=0$

Exercise #2

$(x-1)^2=x^2$

Video Solution

Answer

$x=\frac{1}{2}$

Exercise #3

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

Video Solution

Answer

$x=2$

Exercise #4

$x^2+(x-2)^2=2(x+1)^2$

Video Solution

Answer

$x=\frac{1}{4}$

Exercise #5

$(x+3)^2=(x-3)^2$

Video Solution

Answer

$x=0$

Question 1

Solve the following equation:

$\frac{(2x-1)^2}{x-2}+\frac{(x-2)^2}{2x-1}=4.5x$

Exercise #6

Solve the following equation:

$\frac{(2x-1)^2}{x-2}+\frac{(x-2)^2}{2x-1}=4.5x$

Video Solution

Answer

$-1\pm\sqrt{3}$