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:

(xy)2 (x-y)^2

Video Solution

Step-by-Step Solution

We use the abbreviated multiplication formula:

(xy)(xy)= (x-y)(x-y)=

x2xyyx+y2= x^2-xy-yx+y^2=

x22xy+y2 x^2-2xy+y^2

Answer

x22xy+y2 x^2-2xy+y^2

Exercise #2

(x2)2+(x3)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:

(xy)2=x22xy+y2 (x−y)^2=x^2−2xy+y^2

We apply the formula twice:

(x2)2=x24x+4 (x-2)^2=x^2-4x+4

(x3)2=x26x+9 (x-3)^2=x^2-6x+9

Now we add the two together:

x24x+4+x26x+9= x^2-4x+4+x^2-6x+9=

2x210x+13 2 x^2-10x+13

Answer

2x210x+13 2x^2-10x+13

Exercise #3

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

(x7)2 (x-7)^2

Video Solution

Answer

x214x+49 x^2-14x+49

Exercise #4

(x26)2= (x^2-6)^2=

Video Solution

Answer

x412x2+36 x^4-12x^2+36

Exercise #5

(xx2)2= (x-x^2)^2=

Video Solution

Answer

x42x3+x2 x^4-2x^3+x^2

Exercise #6

9x212x+4= 9x^2-12x+4=

Video Solution

Answer

(3x2)2 (3x-2)^2

Exercise #7

2(3x1)23(2x+1)2= 2(3x-1)^2-3(2x+1)^2=

Video Solution

Answer

6x(x4)1 6x(x-4)-1