Square of The Sum of Two Binomials
How to find the square of the sum of two binomials?
(a + b) (a + b) = a(a + b) + b(a + b)
= a2 + ab + ba + b2
= a2 + 2ab + b2
= a2 + b2+ 2ab
Therefore, (a + b)2 = a2 + b2 + 2ab
Square of the sum of two terms = square of 1st term + square of 2nd term + 2 × fist term × second term
This is called the binomial square.
It is stated as: the Square of the binomial (sum of two unlike term) is the square of the first term plus the square of the second term plus twice the product of two terms.
Worked-out examples on square of the sum of two binomials:
Solution:
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 2x and b = 3y
= (2x)2 + (3y)2 + 2 (2x) (3y)
= 4x2 + 9y2 + 12xy
Therefore, (2x + 3y)2 = 4x2 + 9y2 + 12xy.
2. Evaluate 1052 using the formula of (a + b)2.
Solution:
1052 = (100 + 5)2
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 100 and b = 5
(100 + 5)2
= (100)2 + (5)2 + 2 (100) (5)
= 10000 + 25 + 1000
= 11025
Therefore, 1052 = 11025.
3. Evaluate (10.1)2 using the identity.
Solution:
(10.1)2 = (10 + 0.1)2
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 10 and b = 0.1
(10 + 0.1)2
= (10)2 + (0.1)2 + 2 (10) (0.1)
= 100 + 0.01 + 2
= 102.01
Therefore, (10.1)2 = 102.01.
4. Use the formula of square of the sum of two terms to find the product of (1/5 x + 3/2 y) (1/5 x + 3/2 y).
Solution:
(1/5 x + 3/2 y) (1/5 x + 3/2 y) = (1/5 x + 3/2 y)2
We know that (a + b)2 = a2 + b2 + 2ab
Here, a = 1/5 x and b = 3/2 y
= (1/5 x)2 + (3/2 y)2 +
= 1/25 x2 + 9/4 y2 + 3/5 xy
Therefore, (1/5 x + 3/2 y) (1/5 x + 3/2 y) = 1/25 x2 + 9/4 y2 + 3/5 xy.
From the above solved problems we come to know square of a number means multiplying a number with itself, similarly, square of the sum of two binomial means multiplying the binomial with itself.
7th Grade Math Problems
8th Grade Math Practice
From Square of The Sum 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.
Recent Articles
-
2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line
Dec 14, 24 02:12 PM
2nd grade geometry worksheet -
2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic
Dec 14, 24 12:25 PM
2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. -
Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns
Dec 13, 24 08:43 AM
We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r… -
Patterns in Math | Missing Number | Counting Numbers | Worksheets
Dec 13, 24 12:31 AM
Finding patterns in math is very important to understand the sequence in the series. We need to find the exact missing number that from the group of numbers. The counting numbers may be counting -
Concept of Pattern | Similar Patterns in Mathematics | Similar Pattern
Dec 12, 24 11:22 PM
Concept of pattern will help us to learn the basic number patterns and table patterns. Animals such as all cows, all lions, all dogs and all other animals have dissimilar features. All mangoes have si…
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.