DIFFERENCE OF TWO SQUARES WORKSHEET

Find the product of two binomials in each case.

Question 1 :

(c + d)(c - d)

Question 2 :

(x + 3)(x - 3)

Question 3 :

(y + √5)(x - √5)

Question 4 :

(3p + 5q)(3p - 5q)

Question 5 :

(x2 + 2y)(x2 - 2y)

Question 6 :

(8 + z)(8 - z)

Question 7 :

(2 + 3x)(2 - 3x)

Question 8 :

(3 + 2z2)(3 + 2z2)

Question 9 :

(a2 + b2)(a2 - b2)

Question 10 :

(2x + yz)(2x - yz)

Answers

1. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = c and b = d. 

(c + d)(c - d)  =  c2 - d2

2. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = x and b = 3. 

(x + 3)(x - 3)  =  x2 - 32

=  x2 - 9

3. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = y and b = √5

(y + √5)(x - √5)  =  y2 - (√5)2

=  y2 - 5

4. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = 3p and b = 5q. 

(3p + 5q)(3p - 5q)  =  (3p)2 - (5q)2

=  9p2 - 25q2

5. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = x2 and b = 2y. 

(x2 + 2y)(x2 - 2y)  =  (x2)2 - (2y)2

=  x4 - 4y2

6. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = 8 and b = z. 

(8 + z)(8 - z)  =  (8)2 - (z)2

=  64 - z2

7. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = 2 and b = √3x

(2 + 3x)(2 - 3x)  =  22 - (√3x)2

=  4 - 3x2

8. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = 3 and b = 2z2

(3 + 2z2)(3 + 2z2)  =  (3)2 - (2z)2

=  9 - 4z2

9. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = a2 and b = b2

(a2 + b2)(a2 - b2)  =  (a2)2 - (b2)2

=  a4 - b4

10. Answer :

Use the rule for (a + b)(a - b). 

(a + b)(a - b)  =  a2 - b2

Identify a and b : a = 2x and b = yz. 

(2x + yz)(2x - yz)  =  (2x)2 - (yz)2

=  4x2 - y2z2

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