All the students who are unable to understand the concept of Expansion of Powers of Binomials and Trinomials can refer to our page and learn the topics quickly and easily. Enhance your math skills by solving the problems from Worksheet on Expansion of (a ± b)^2 and its Corollaries. Practice the questions from here and secure the highest marks in the exams. Step-by-step explanations for all the questions are provided in the simple techniques in this Worksheet on Expansion of (a ± b)² and its Corollaries.
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Expansion of (a ± b)^2 and its Corollaries Worksheet PDF
Check out the questions given below and try to solve the problems quickly.
Example 1.
Simplify (4m + 6n)² + (4m – 6n)²
Solution:
Given that
(4m + 6n)² + (4m – 6n)²
We know that
The formula of (a + b)² + (a – b)² = 2(a² + b²)
2{(4m)² + (6n)²}
2(16m² + 36n²)
32m² + 72n²
Thus (4m + 6n)² + (4m – 6n)² is 32m² + 72n²
Example 2.
Expand (4a + 1/4a)² by using (a + b)² formula.
Solution:
Given that
(4a + 1/4a)²
We know that
The formula of (a + b)² + (a – b)² = 2(a² + b²)
(4a)² + 4 × 4p × 1/4p + (1/4p)²
16a² + 4 + (1/16p²)
Thus the expansion of (4a + 1/4a)² is 16a² + 4 + (1/16p²)
Example 3.
Expand (5a + 2b)² by using the (a + b)² formula.
Solution:
Given that
(5a + 2b)²
We know that
The formula of (a + b)² + (a – b)² = 2(a² + b²)
(5a)² + 2 × 5a × 2b + (2b)²
25a² + 20ab + 4b²
Thus the expansion of (5a + 2b)² is 25a² + 20ab + 4b²
Example 4.
Simply the equation (a + 1/a)² + (a + 1/a)².
Solution:
We know that
The formula of (a + b)² + (a – b)² = 2(a² + b²)
2(a² – 1/a² + a² + 1/a²)
2(a² – 1/a² + a² + 1/a²)
2(2a²)
4a²
Thus (a + 1/a)² + (a + 1/a)² is 4a²
Example 5.
If a + b = 4 and ab = 2. Find a² + b²
Solution:
We know that
The formula of a² + b² = (a + b)² – 2ab
a² + b² = (4)² – 2(2)
16 – 4
12
Thus the value of the expression a² + b² is 12.
Example 6.
If x + y = 8 and x – y = 4 evaluate xy
Solution:
Given,
x + y = 8 and x – y = 4
We know that
xy = (x + y)(x – y)
xy = 8 × 4
xy = 32
Therefore the value of xy is 32.
Example 7.
If a + 1/a = 2 find the value of a⁴ + 1/a⁴.
Solution:
Given,
a + 1/a = 2
We notice that
(a + 1/a)² = 2² = 4
But
(a + 1/a)² = a² + (1/a)² + 2 × a(1/a)
= a² + 1/a² + 2 = 4
a² + 1/a² = 4 – 2 = 2
Again
(a² + 1/a²)² = 2² = 4
Know
(a² + 1/a²)² = a⁴ + 2(a²)(1/a)² + 1/a⁴
a⁴ + 2 + 1/a⁴
a⁴ + 1/a⁴ + 2 = 4
a⁴ + 1/a⁴ = 2
Thus a⁴ + 1/a⁴ = 2
Example 8.
Expand the equation (2x – 3y)² by using the (a – b)² formula.
Solution:
Given that
(2x – 3y)²
We know that
The formula of (a – b)² = a² + b² + 2ab
(2x)² + (3y)² – 2(2x)(3y)
4x² + 9y² – 12xy
Thus (2x – 3y)² is 4x² + 9y² – 12xy
Example 9.
Expand the squares of ½ + 4/2n by using the (a + b)² formula.
Solution:
Given that
½ + 4/2 n
We know that
The formula of (a + b)² = a² + b² + 2ab
(½)² + (4/2 n)² + 2 × ½ × 4/2 n
¼ + 16/4 n² + 2n
¼ + 4n² + 2n
¼ + 2n + 4n²
Thus the squares of ½ + 4/2n is ¼ + 2n + 4n²
Example 10.
Expand the squares of the 2x + y by using the (a + b)² formula.
Solution:
Given that,
2x + y
Square of the 2x + y = (2x + y)²
We know that
The formula of (a + b)² = a² + b² + 2ab
(2x)² + y² + 2xy
4x² + 2xy + y²
Thus squares of the 2x + y is 4x² + 2xy + y²