The formula for the difference of squares

πŸ†Practice the formula of the difference of squares

(Xβˆ’Y)2=X2βˆ’2XY+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.

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Test yourself on the formula of the difference of squares!

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Declares the given expression as a sum

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

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Pay attention - The formula also works in non-algebraic expressions or combinations with numbers and unknowns.

Let's look at an example

(Xβˆ’7)2=(X-7)^2=
Here we identify two elements between which there is a minus sign and they are enclosed in parentheses and raised to the square as a single expression.
Therefore, we can use the formula for the difference of squares.
We will work according to the formula and pay attention to the minus and plus signs.
We will obtain:Β 
(Xβˆ’7)2=x2βˆ’14x+49(X-7)^2=x^2-14x+49
Indeed, we pronounce the same expression differently using the formula.


If you are interested in this article, you might also be interested in the following articles:

Square

The area of a square

Multiplication of the sum of two elements by the difference between them

The formula for the sum of squares

The formulas that refer to two expressions to the power of 3

In the blog of Tutorela you will find a variety of articles about mathematics.


Examples and exercises with solutions of the difference of squares formula

Exercise #1

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

(xβˆ’y)2 (x-y)^2

Video Solution

Step-by-Step Solution

We use the abbreviated multiplication formula:

(xβˆ’y)(xβˆ’y)= (x-y)(x-y)=

x2βˆ’xyβˆ’yx+y2= x^2-xy-yx+y^2=

x2βˆ’2xy+y2 x^2-2xy+y^2

Answer

x2βˆ’2xy+y2 x^2-2xy+y^2

Exercise #2

(xβˆ’2)2+(xβˆ’3)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:

(xβˆ’y)2=x2βˆ’2xy+y2 (xβˆ’y)^2=x^2βˆ’2xy+y^2

Now, we apply this property twice:

(xβˆ’2)2=x2βˆ’4x+4 (x-2)^2=x^2-4x+4

(xβˆ’3)2=x2βˆ’6x+9 (x-3)^2=x^2-6x+9

Now we add:

x2βˆ’4x+4+x2βˆ’6x+9= x^2-4x+4+x^2-6x+9=

2x2βˆ’10x+13 2 x^2-10x+13

Answer

2x2βˆ’10x+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=(xβˆ’7)2 A=(x-7)^2

Answer

(xβˆ’7)2 (x-7)^2

Exercise #4

Declares the given expression as a sum

(7bβˆ’3x)2 (7b-3x)^2

Video Solution

Answer

49b2βˆ’42bx+9x2 49b^2-42bx+9x^2

Exercise #5

(4bβˆ’3)(4bβˆ’3) (4b-3)(4b-3)

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

Video Solution

Answer

(4bβˆ’3)2 (4b-3)^2

16b2βˆ’24b+9 16b^2-24b+9

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