FACTORING THE DIFFERENCE OF TWO SQUARES WORKSHEET

Factor each of the following :

Question 1 :

y² - 16

Question 2 :

49 - x²

Question 3 :

9p² - 64

Question 4 :

y² - 4z²

Question 5 :

25r² - t²

Question 6 :

100x² - 81y²

Question 7 :

0.25x² - 0.36y²

Question 8 :

0.04m² - 0.09n²

Question 9 :

3x² - y²

Question 10 :

4p² - 5q²

Question 11 :

2m² - 3n²

Question 12 :

x - y

Question 13 :

3p² - 4q

Question 14 :

p⁴ - q⁴

Answers

1. Answer :

y² - 16 = y² - 4²

Comparing a² - b² and y² - 4²,

a = y and b = 4

We know that

a² - b² = (a + b)(a - b)

Substitute a = y and b = 4.

y² - 4² = (y + 4)(y - 4)

y² - 16 = (y + 4)(y - 4)

2. Answer :

49 - x² = 7² - x²

Comparing a² - b² and 7² - x²,

a = 7 and b = x

We know that

a² - b² = (a + b)(a - b)

Substitute a = 7 and b = x.

7² - x² = (7 + x)(7 - x)

49 - x² = (7 + x)(7 - x)

3. Answer :

9p² - 64 = 3²p² - 8²

= (3p)² - 8²

Comparing a² - b² and (3p)² - 8²,

a = 3p and b = 8

We know that

a² - b² = (a + b)(a - b)

Substitute a = 3p and b = 8.

(3p)² - 8² = (3p + 8)(3p - 8)

9p² - 64 = (3p + 8)(3p - 8)

4. Answer :

y² - 4z² = y² - 2²z²

= y² - (2z)²

Comparing a² - b² and y² - (2z)²,

a = y and b = 2z

We know that

a² - b² = (a + b)(a - b)

Substitute a = y and b = 2z.

y² - (2z)² = (y + 2z)(y - 2z)

y² - 4z² = (y + 2z)(y - 2z)

5. Answer :

25r² - t² = 5²r² - t²

= (5r)² - t²

Comparing a² - b² and (5r)² - t²,

a = 5r and b = t

We know that

a² - b² = (a + b)(a - b)

Substitute a = 5r and b = t.

(5r)² - t² = (5r + t)(5r - t)

25r² - t² = (5r + t)(5r - t)

6. Answer :

100x² - 81y² = 10²x² - 9²y²

= (10x)² - (9y)²

Comparing a² - b² and (10x)² - (9y)²,

a = 10x and b = 9y

We know that

a² - b² = (a + b)(a - b)

Substitute a = 10x and b = 9y.

(10x)² - (9y)² = (10x + 9y)(10x - 9y)

100x² - 81y² = (10x + 9y)(10x - 9y)

7. Answer :

0.25x² - 0.36y² = 0.5²x² - 0.6²y²

= (0.5x)² - (0.6y)²

Comparing a² - b² and (0.5x)² - (0.6y)²,

a = 0.5x and b = 0.6y

We know that

a² - b² = (a + b)(a - b)

Substitute a = 0.5x and b = 0.6y.

(0.5x)² - (0.6y)² = (0.5x + 0.6y)(0.5x - 0.6y)

0.25x² - 0.36y² = (0.5x + 0.6y)(0.5x - 0.6y)

8. Answer :

0.04m² - 0.09n² = 0.2²m² - 0.3²n²

= (0.2m)² - (0.3n)²

Comparing a² - b² and (0.2m)² - (0.3n)²,

a = 0.2m and b = 0.3n

We know that

a² - b² = (a + b)(a - b)

Substitute a = 0.2m and b = 0.3n.

(0.2m)² - (0.3n)² = (0.2m + 0.3n)(0.2m - 0.3n)

0.04m² - 0.09n² = (0.2m + 0.3n)(0.2m - 0.3n)

9. Answer :

3x² - y² = (√3)²x² - y²

= (√3x)² - y²

Comparing a² - b² and (√3x)² - y²,

a = √3x and b = y

We know that

a² - b² = (a + b)(a - b)

Substitute a = √3x and b = y.

(√3x)² - y² = (√3x + y)(√3x - y)

3x² - y² = (√3x + y)(√3x - y)

10. Answer :

4p² - 5q² = 2²p² - (√5)²q²

= (2p)² - (√5q)²

Comparing a² - b² and (√3x)² - y²,

a = 2p and b = √5q

We know that

a² - b² = (a + b)(a - b)

Substitute a = 2p and b = √5q.

(2p)² - (√5q)² = (2p + √5q)(2p - √5q)

4p² - 5q² = (2p + √5q)(2p - √5q)

11. Answer :

2m² - 3n² = (√2)²m² - (√3)²n²

= (√2m)² - (√3n)²

Comparing a² - b² and (√2m)² - (√3n)²,

a = √2m and b = √3n

We know that

a² - b² = (a + b)(a - b)

Substitute a = √2m and b = √3n.

(√2m)² - (√3n)² = (√2m + √3n)(√2m - √3n)

2m² - 3n² = (√2m + √3n)(√2m - √3n)

12. Answer :

x - y = (√x)² - (√y)²

Comparing a² - b² and (√x)² - (√y)²,

a = √x and b = √y

We know that

a² - b² = (a + b)(a - b)

Substitute a = √x and b = √y.

(√x)² - (√y)² = (√x + √y)(√x - √y)

x - y = (√x + √y)(√x - √y)

13. Answer :

3p² - 4q = (√3)²p² - 2²(√q)²

= (√3p)² - (2√q)²

Comparing a² - b² and (√3p)² - (2√q)²,

a = √3p and b = 2√q

We know that

a² - b² = (a + b)(a - b)

Substitute a = √3p and b = 2√q.

(√3p)² - (2√q)² = (√3p + 2√q)(√3p - 2√q)

3p² - 4q = (√3p + 2√q)(√3p - 2√q)

14. Answer :

p⁴ - q⁴ = (p²)² - (q²)²

Comparing a² - b² and (p²)² - (q²)²,

a = p² and b = q²

We know that

a² - b² = (a + b)(a - b)

Substitute a = p² and b = q².

(p²)² - (q²)² = (p² + q²)(p² - q²)

p⁴ - q⁴ = (p² + q²)(p + q)(p - q)

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