Product of Sum and Difference of Two Binomials

How to find the product of sum and difference of two binomials with the same terms and opposite signs?



(a + b) (a – b) = a(a – b) + b (a – b)

                     = a2ab + ba + b2

                     = a2 – b2

Therefore (a + b) (a – b) = a2 – b2

(First term + Second term) (First term – Second term) = (First term)2 – (Second term) 2

It is stated as: The product of the binomial sum and difference is equal to the square of the first term minus the square of the second term.

Worked-out examples on the product of sum and difference of two binomials:

1. Find the product (2x + 7y) (2x – 7y) by using the identity.

Solution:

We know (a + b) (a – b) = a2 – b2

Here a = 2x and b= 7y

= (2x)2 – (7y)2

= 4x2 – 49y2

Therefore, (2x + 7y)(2x – 7y) = 4x2 – 49y2


2. Evaluate 502 – 492 using the identity

Solution:

We know a2 – b2 = (a + b)(a – b)

Here a = 50, b = 49

= (50 + 49) (50 – 49)

= 99 × 1

= 99

Therefore, 502 – 492 = 99


3. Simplify 63 × 57 by expressing it as the product of binomial sum and difference.

Solution:

63 × 57 = (60 + 3) (60 – 3)

We know (a + b) (a – b) = a2 – b2

= (60)2 – (3)2

= 3600 – 9

= 3591

Therefore, 63 × 57 = 3591


4. Find the value of x if 232 – 172 = 6x

Solution:

We know a2 – b2 = (a + b) (a – b)

Here a = 23 and b = 17

Therefore 232 – 172 = 6x

(23 + 17)(23 – 17) = 6x

40 × 6 = 6x

240 = 6x

6x/6 = 240/6

Therefore, x = 40


5. Simplify 43 × 37 by expressing it as a difference of two squares.

Solution:

43 × 37 = (40 + 3)( 40 – 3)

We know (a + b) (a – b) = a2 – b2

Here a = 40 and b = 3

= (40)2 – (3)2

= 1600 – 9

= 1591

Therefore, 43 × 37 = 1591

Thus, the product of sum and difference of two binomials is equal to the square of the first term minus the square of the second term.





7th Grade Math Problems

8th Grade Math Practice

From Product of Sum and Difference of Two Binomials to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

    Apr 18, 24 02:15 AM

    What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

    Read More

  2. Simple Closed Curves | Types of Closed Curves | Collection of Curves

    Apr 18, 24 01:36 AM

    Closed Curves Examples
    In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.

    Read More

  3. Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles

    Apr 18, 24 12:31 AM

    Tangrams
    Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…

    Read More

  4. Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

    Apr 17, 24 01:32 PM

    Duration of Time
    We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton every evening. Yesterday, their game started at 5 : 15 p.m.

    Read More

  5. Worksheet on Third Grade Geometrical Shapes | Questions on Geometry

    Apr 16, 24 02:00 AM

    Worksheet on Geometrical Shapes
    Practice the math worksheet on third grade geometrical shapes. The questions will help the students to get prepared for the third grade geometry test. 1. Name the types of surfaces that you know. 2. W…

    Read More