Square of Difference: Using multiple rules

Equations with denominatorsUsing quadrilateralsComplete the missing numbersData with powers and rootsMore than one factorizationNumber of termsIdentify the greater valueUsing fractionsEquations with variables on both sidesResulting in a quadratic equationSystem of equations with no solutionSolving the problemTransition between expressions
Question 1

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

Question 2

\( (x+y)^2-(x-y)^2+(x-y)(x+y)=\text{?} \)

Question 3

\( (x+3)^2+(x-3)^2=\text{?} \)

Question 4

\( (a+3b)^2-(3b-a)^2=\text{?} \)

Question 5

Find a X given the following equation:

\( (x+3)^2+(2x-3)^2=5x(x-\frac{3}{5}) \)

Examples with solutions for Square of Difference: Using multiple rules

Exercise #1

(x+3)2=(x−3)2 (x+3)^2=(x-3)^2

Video Solution

Step-by-Step Solution

Let's examine the given equation:

(x+3)2=(x−3)2 (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±b)2=a2±2ab+b2 (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↓x2+2⋅x⋅3+32=x2−2⋅x⋅3+32x2+6x+9=x2−6x+9x2+6x+9−x2+6x−9=012x=0/:12x=0 (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 x=0

Exercise #2

(x+y)2−(x−y)2+(x−y)(x+y)=? (x+y)^2-(x-y)^2+(x-y)(x+y)=\text{?}

Video Solution

Answer

x2+4xy−y2 x^2+4xy-y^2

Exercise #3

(x+3)2+(x−3)2=? (x+3)^2+(x-3)^2=\text{?}

Video Solution

Answer

2x2+18 2x^2+18

Exercise #4

(a+3b)2−(3b−a)2=? (a+3b)^2-(3b-a)^2=\text{?}

Video Solution

Answer

12ab 12ab

Exercise #5

Find a X given the following equation:

(x+3)2+(2x−3)2=5x(x−35) (x+3)^2+(2x-3)^2=5x(x-\frac{3}{5})

Video Solution

Answer

6 6

Question 1

\( (\frac{x}{3}-4)^2+x(\frac{\sqrt{8x}}{3}+2)(\frac{\sqrt{8x}}{3}-2)=\text{?} \)

Question 2

\( (\frac{2}{3}+\frac{m}{4})^2-\frac{4}{3}-(\frac{m}{4}-\frac{2}{3})^2=\text{?} \)

Exercise #6

(x3−4)2+x(8x3+2)(8x3−2)=? (\frac{x}{3}-4)^2+x(\frac{\sqrt{8x}}{3}+2)(\frac{\sqrt{8x}}{3}-2)=\text{?}

Video Solution

Answer

x2−623x+16 x^2-6\frac{2}{3}x+16

Exercise #7

(23+m4)2−43−(m4−23)2=? (\frac{2}{3}+\frac{m}{4})^2-\frac{4}{3}-(\frac{m}{4}-\frac{2}{3})^2=\text{?}

Video Solution

Answer

(2m+2)(2m−2)3 \frac{(\sqrt{2m}+2)(\sqrt{2m}-2)}{3}