The formula of the difference of squares - Examples, Exercises and Solutions

(XY)2=X22XY+Y2(X - Y)2=X2 - 2XY + Y2
This is one of the shortened multiplication formulas and it describes the square difference of two numbers.

That is, when we encounter two numbers with a minus sign between them, that is, the difference and they will be in parentheses and raised as a squared expression, we can use this formula.

Suggested Topics to Practice in Advance

  1. The formula for the sum of squares

Practice The formula of the difference of squares

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

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

Now, we apply this property 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:

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

Look at the square below:

AAABBBDDDCCCX-7

Express its area in terms of x x .

Video Solution

Step-by-Step Solution

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

The formula for the area of the square is

A=L2 A=L^2

We place the data in the formula:

A=(x7)2 A=(x-7)^2

Answer

(x7)2 (x-7)^2

Exercise #4

Declares the given expression as a sum

(7b3x)2 (7b-3x)^2

Video Solution

Answer

49b242bx+9x2 49b^2-42bx+9x^2

Exercise #5

(4b3)(4b3) (4b-3)(4b-3)

Write the above as a power expression and as a summation expression.

Video Solution

Answer

(4b3)2 (4b-3)^2

16b224b+9 16b^2-24b+9

Exercise #1

Rewrite the following expression as an addition and as a multiplication:

(3xy)2 (3x-y)^2

Video Solution

Answer

9x26xy+y2 9x^2-6xy+y^2

(3xy)(3xy) (3x-y)(3x-y)

Exercise #2

(a4)(a4)=? (a-4)(a-4)=\text{?}

Video Solution

Answer

a28a+16 a^2-8a+16

Exercise #3

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

Video Solution

Answer

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

Exercise #4

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 #5

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

Video Solution

Answer

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

Exercise #1

x2+144=24x x^2+144=24x

Video Solution

Answer

x=12 x=12

Exercise #2

x2=6x9 x^2=6x-9

Video Solution

Answer

x=3 x=3

Exercise #3

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

Video Solution

Answer

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

Exercise #4

x22x+1=9 x^2-2x+1=9

Solve using the abbreviated multiplication formula

Video Solution

Answer

x=2 x=-2 o x=4 x=4

Exercise #5

(x4)2=(x+2)(x1) (x-4)^2=(x+2)(x-1)

Video Solution

Answer

x=2 x=2

Topics learned in later sections

  1. Abbreviated Multiplication Formulas
  2. Multiplication of the sum of two elements by the difference between them