## SQUARE OF A BINOMIAL WORKSHEET

Square of a Binomial Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on finding square of a binomial.

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Formula for (a + b)2

Formula for (a - b)2

## Square of a Binomial Worksheet - Problems

Problem 1 :

Expand :

(x + 2)2

Problem 2 :

Expand :

(x - 5)2

Problem 3 :

Expand :

(5x + 3)2

Problem 4 :

Expand :

(5x - 3)2

Problem 5 :

If a + b  =  7 and a2 + b2  =  29, then find the value of ab.

Problem 6 :

If a - b  =  3 and a2 + b2  =  29, then find the value of ab.

Problem 7 :

Find the value of :

(√2 + 1/√2)2

Problem 8 :

Find the value of :

(√2 - 1/√2)2

Problem 9 :

Find the value of :

(105)2

Problem 10 :

Find the value of :

(95)2 ## Square of a Binomial Worksheet - Solutions

Problem 1 :

Expand :

(x + 2)

Solution :

(x + 2)is in the form of (a + b)2

Comparing (a + b)and (x + 2)2, we get

a  =  x

b  =  2

Write the formula / expansion for (a + b)2.

(a + b)2  =  a2 + 2ab + b2

Substitute x for a and 2 for b.

(x + 2)2  =  x2 + 2(x)(2) + 32

(x + 2)2  =  x2 + 4x + 9

So, the expansion of (x + 2)2 is

x2 + 4x + 9

Problem 2 :

Expand :

(x - 5)

Solution :

(x - 5)is in the form of (a - b)2

Comparing (a - b)and (x - 5)2, we get

a  =  x

b  =  5

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute x for a and 5 for b.

(x - 5)2  =  x2 - 2(x)(5) + 52

(x - 5)2  =  x2 - 10x + 25

So, the expansion of (x - 5)2 is

x2 - 10x + 25

Problem 3 :

Expand :

(5x + 3)

Solution :

(5x + 3)is in the form of (a + b)2

Comparing (a + b)and (5x + 3)2, we get

a  =  5x

b  =  3

Write the expansion for (a + b)2.

(a + b)2  =  a2 + 2ab + b2

Substitute 5x for a and 3 for b.

(5x + 3)2  =  (5x)2 + 2(5x)(3) + 32

(5x + 3)2  =  25x2 + 30x + 9

So, the expansion of (5x + 3)2 is

25x2 + 30x + 9

Problem 4 :

Expand :

(5x - 3)

Solution :

(5x - 3)is in the form of (a - b)2

Comparing (a - b)and (5x - 3)2, we get

a  =  5x

b  =  3

Write the expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute 5x for a and 3 for b.

(5x - 3)2  =  (5x)2 - 2(5x)(3) + 32

(5x - 3)2  =  25x2 - 30x + 9

So, the expansion of (5x - 3)2 is

25x2 - 30x + 9

Problem 5 :

If a + b  =  7 and a2 + b2  =  29, then find the value of ab.

Solution :

To get the value of ab, we can use the formula or expansion of (a + b)2.

Write the formula / expansion for (a + b)2.

(a + b)2  =  a2 + 2ab + b2

or

(a + b)2  =  a2 + b2 + 2ab

Substitute 7 for (a + b)  and 29 for (a2 + b2).

72  =  29 + 2ab

49  =  29 + 2ab

Subtract 29 from each side.

20  =  2ab

Divide each side by 2.

10  =  ab

So, the value of ab is 10.

Problem 6 :

If a - b  =  3 and a2 + b2  =  29, then find the value of ab.

Solution :

To get the value of ab, we can use the formula or expansion of (a - b)2.

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

or

(a - b)2  =  a2 + b- 2ab

Substitute 3 for (a - b)  and 29 for (a2 + b2).

32  =  29 - 2ab

9  =  29 - 2ab

Subtract 29 from each side.

-20  =  -2ab

Divide each side by (-2).

10  =  ab

So, the value of ab is 10.

Problem 7 :

Find the value of :

(√2 + 1/√2)2

Solution :

(√2 + 1/√2)2 is in the form of (a + b)2

Comparing (a + b)and (√2 + (1/√2)2, we get

a  =  √2

b  =  1/√2

Write the expansion for (a + b)2.

(a + b)2  =  a2 + 2ab + b2

Substitute √2 for a and 1/√2 for b.

(√2
+ 1/√2)2  =  (√2)2 + 2(√2)(1/√2) + (1/√2)2

(√2 + 1/√2)2  =  2 + 2 + 1/2

(√2 + 1/√2)2  =  9/2

So, the value of (√2 + 1/√2)2 is

9 / 2

Problem 8 :

Find the value of :

(√2 - 1/√2)2

Solution :

(√2 - 1/√2)2 is in the form of (a - b)2

Comparing (a - b)and (√2 - 1/√2)2, we get

a  =  √2

b  =  1/√2

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute √2 for a and 1/√2 for b.

(√2
- 1/√2)2  =  (√2)2 - 2(√2)(1/√2) + (1/√2)2

(√2 - 1/√2)2  =  2 - 2 + 1/2

(√2 - 1/√2)2  =  1/2

So, the value of (√2 - 1/√2)is

1 / 2

Problem 9 :

Find the value of :

(105)2

Solution :

Instead of multiplying 105 by 105 to get the value of (105)2, we can use the algebraic formula for (a + b)2 and find the value of (105)easily.

Write (105)in the form of (a + b)2.

(105)2  =  (100 + 5)2

Write the expansion for (a + b)2.

(a + b)2  =  a2 + 2ab + b2

Substitute 100 for a and 5 for b.

(100 + 5)2  =  (100)2 + 2(100)(5) + (5)2

(100 + 5)2  =  10000 + 1000 + 25

(105)2  =  11025

So, the value of (105)2 is

11025

Problem 10 :

Find the value of :

(95)2

Solution :

Instead of multiplying 95 by 95 to get the value of (95)2, we can use the algebraic formula for (a - b)and find the value of (95)easily.

Write (95)in the form of (a - b)2.

(95)2  =  (100 - 5)2

Write the formula / expansion for (a - b)2.

(a - b)2  =  a2 - 2ab + b2

Substitute 100 for a and 5 for b.

(100
- 5)2  =  (100)2 - 2(100)(5) + (5)2

(100 - 5)2  =  10000 - 1000 + 25

(95)2  =  9025

So, the value of (95)2 is

9025 After having gone through the stuff given above, we hope that the students would have understood the formula or expansion of (a + b)2 and the example problems on expansion of (a + b)2.

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