Worksheet on Expansion of (x ± a)(x ± b) is available on this page for free of cost. Practice the questions given in this article to score the highest marks in the exams. We can solve the problems by using different types of formulas like (x + a)(x – b), (x + a) (x + b), (x – a)(x – b), (x – a) (x + b). The students of 9th grade can learn different types of problems in Expansion of Powers of Binomials and Trinomials.

Expansion of (x ± a)(x ± b) Worksheet PDF

Example 1.
Find the product of (x + 1) (x + 2) using the standard formula.

Solution:

Given that
(x + 1) ( x + 2)
By using the formula (x + a)(x + b) = x² + x(a + b) + ab we can expand the given expression.
Multiply (x + 1) with (x + 2) then we get
x² + 2x + x + 2
x² + 3x + 2
Therefore the solution is x² + 3x + 2

Example 2.
Find the product of ( 2x + 4) ( x – 2) using the standard formula.

Solution:

Given that
(2x + 4) (x – 2)
Multiply (2x + 4) with (x – 2) then we get
2x² – 4x + 4x – 8
2x² – 8
Therefore the solution is 2x² – 8

Example 3.
Find the product of (x + 2) (x + 4) using the standard formula.

Solution:

Given that
(x + 2) (x + 4)
We know that
By using the formula (x + a)(x + b) = x² + x(a + b) + ab we can expand the given expression.
Then we get
(x + 2) (x + 4) = x² + (2 + 4)x + 2 × 4
x² + 6x + 8
Therefore the solution is x² + 6x + 8

Example 4.
Find the product of (4m + n -2) ( 4m + n +1) using the standard formula.

Solution:

Given that
(4m + n -2) ( 4m + n +1)
Let 4m + n = x
Product = ( x – 2) (x + 1)
x² + (-2 + 1)x + (-2)(1)
x² – x – 2
Now x = 4m + n = x
(4m + n)² – (4m + n)- 2
4m² + n² – 4m + n – 2
4m² -4m + n² + n – 2
Therefore the solution is 4m² -4m + n² + n – 2

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Example 5.
Find the product of (a – 4) (a + 6) using the standard formula.

Solution:

Given that
(a – 4) ( a + 6)
We know that
(x + a) ( x + b) = x² + (a + b)x + ab
Then we get
(a – 4) ( a + 6) = a² + (-4 + 6)a + (-4)(6)
a² + 2a – 24
Therefore the solution is a² + 2a – 24

Example 6.
Find the product of (3x + 1) (3x + 2) using the standard formula.

Solution:

Given that
(2x + 1) ( 3x + 2)
We know that
(x + a) ( x + b) = x² + (a + b)x + ab
Then we get
(3x + 1) ( 3x + 2) = 3x² + ( 1 + 2)3x + (1)(2)
3x² + 9x + 3
Therefore the solution is 3x² + 9x + 3

Example 7.
Find the product of ( 4x – y) ( 4x – y) using the standard formula.

Solution:

Given that
(4x – y) (4x – y)
We know that
By using the formula (x – a)(x – b) = x² – x(a + b) + ab
Then we get
(4x – y) ( 4x – y) = 4x² + ( (-1) + (-1))x + (-1)(-1)
= 4x² – 2x – 2
Therefore the solution is 4x² – 2x – 2

Example 8.
Find the product of ( 2x – y + 2) ( 2x – y -3) using the standard formula.

Solution:

Given that
( 2x – y + 2) ( 2x – y -3)
Let 2x – y = x
Product = ( x + 2) (x – 3)
By using the formula (x + a)(x + b) = x² + x(a + b) + ab we can expand the given expression.
x² + (2 – 3)x + (2)(-3)
x² – x – 6
Now x = 2x – y = x
(2x – y)² – (2x – y)² – 6
2x² – y² – 2x – y² – 6
2x² – 2y² – 2x – 6
Therefore the solution is 2x² – 2y² – 2x – 6

Example 9.
Find the product of (x + y + 3) (x + y + 4) using the standard formula.

Solution:

Given that
(x + y + 3) ( x + y + 4)
Let x + y = x
Product = ( x + 3) ( x + 4)
By using the formula (x + a)(x + b) = x² + x(a + b) + ab we can expand the given expression.
x² + 4x + 3x + 12
x² + 7x + 12
Now x = x + y
(x + y) + 4(x + y) + 3(x + y) + 12
x + y + 4x + 4y + 3x + 3y + 12
8x + 8y + 12
Therefore the solution is 8x + 8y + 12.

Example 10.
Find the product of (2x + 1) (2x + 2) using the standard formula.

Solution:

Given that
(2x + 1) ( 2x + 2)
By using the formula (x + a)(x + b) = x² + x(a + b) + ab we can expand the given expression.
Multiply (2x + 1) with (2x + 2) then we get
4x² + 4x + 2x + 2
4x² + 6x + 2
Therefore the solution is 4x² + 6x + 2.