Square of Difference: System of equations with no solution

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 equationUsing multiple rulesSolving the problemTransition between expressions
Question 1

Choose the expression that has the same value as the following:

\( (x-y)^2 \)

Question 2

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

Question 3

Choose the expression that has the same value as the following:

\( (x-7)^2 \)

Question 4

\( (x^2-6)^2= \)

Question 5

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

Examples with solutions for Square of Difference: System of equations with no solution

Exercise #1

Choose the expression that has the same value as the following:

(x−y)2 (x-y)^2

Video Solution

Step-by-Step Solution

We use the abbreviated multiplication formula:

(x−y)(x−y)= (x-y)(x-y)=

x2−xy−yx+y2= x^2-xy-yx+y^2=

x2−2xy+y2 x^2-2xy+y^2

Answer

x2−2xy+y2 x^2-2xy+y^2

Exercise #2

(x−2)2+(x−3)2= (x-2)^2+(x-3)^2=

Video Solution

Step-by-Step Solution

In order to solve the question, we need to know one of the shortcut multiplication formulas:

(x−y)2=x2−2xy+y2 (x−y)^2=x^2−2xy+y^2

We apply the formula twice:

(x−2)2=x2−4x+4 (x-2)^2=x^2-4x+4

(x−3)2=x2−6x+9 (x-3)^2=x^2-6x+9

Now we add the two together:

x2−4x+4+x2−6x+9= x^2-4x+4+x^2-6x+9=

2x2−10x+13 2 x^2-10x+13

Answer

2x2−10x+13 2x^2-10x+13

Exercise #3

Choose the expression that has the same value as the following:

(x−7)2 (x-7)^2

Video Solution

Answer

x2−14x+49 x^2-14x+49

Exercise #4

(x2−6)2= (x^2-6)^2=

Video Solution

Answer

x4−12x2+36 x^4-12x^2+36

Exercise #5

(x−x2)2= (x-x^2)^2=

Video Solution

Answer

x4−2x3+x2 x^4-2x^3+x^2

Question 1

\( 9x^2-12x+4= \)

Question 2

\( 2(3x-1)^2-3(2x+1)^2= \)

Exercise #6

9x2−12x+4= 9x^2-12x+4=

Video Solution

Answer

(3x−2)2 (3x-2)^2

Exercise #7

2(3x−1)2−3(2x+1)2= 2(3x-1)^2-3(2x+1)^2=

Video Solution

Answer

6x(x−4)−1 6x(x-4)-1