MULTIPLYING CONJUGATE BINOMIALS WORKSHEET

Problems 1-10 : Expand and simplify.

Problem 1 :

(y + 3)(y - 3)

Problem 2 :

(3x - 1)(3x + 1)

Problem 3 :

(1 + √2)(1 - √2)

Problem 4 :

(√3 - 5)(√3 + 5)

Problem 5 :

(3√2 - 1)(3√2 - 1)

Problem 6 :

(√3 + √2)(√3 - √2)

Problem 7 :

(3√p - 2)(3√p + 2)

Problem 8 :

(√a + 2√b)(√a - 2√b)

Problem 9 :

(2a + 3b)(2a - 3b)

Problem 10 :

(p² - 5q)(p² + 5q)

Problem 11 :

(8a² - 2)(8a² + 2)

Problem 12 :

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

Problem 13 :

(-m + 5n)(-m - 5n)

Problem 14 :

(-y + 3x)(-y - 3x)

Problem 15 :

(a² + b²)(a + b)(a - b)

Answers

1. Answer :

= (y + 3)(y - 3)

= y² - 3²

= y² - 9

2. Answer :

= (3x - 1)(3x + 1)

= (3x)² - 1²

= 3²x² - 1

= 9x² - 1

3. Answer :

= (1 + √2)(1 - √2)

= 1² - (√2)²

= 1 - 2

= -1

4. Answer :

= (√3 - 5)(√3 + 5)

= (√3)² - 5²

= 3 - 25

= -22

5. Answer :

= (3√2 - 1)(3√2 - 1)

= (3√2)² - 1²

= 3²(√2)² - 1

= 9(2) - 1

= 18 - 1

= 17

6. Answer :

= (√3 + √2)(√3 - √2)

= (√3)² - (√2)²

= 3 - 2

= 1

7. Answer :

= (3√p - 2)(3√p + 2)

 = (3√p)² - 2²

 = 3²(√p)² - 4

= 9p - 4

8. Answer :

= (√a + 2√b)(√a - 2√b)

= (√a)² - (2√b)²

= a - 2²(√b)²

= a - 4b

9. Answer :

= (2a + 3b)(2a - 3b)

= (2a)² - (3b)²

= 2²a² - 3²b²

= 4a² - 9b²

10. Answer :

= (p² - 5q)(p² + 5q)

= (p²)² - (5q)²

= p⁴ - 5²q²

= p⁴ - 25y²

11. Answer :

= (8a² - 2)(8a² + 2)

= (8a²)² - 2²

= 8²(a²)² - 4

= 64a⁴ - 4

12. Answer :

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

= (0.6x)² - (0.5y)²

= 0.6²x² - 0.5²y²

= 0.36x² - 0.25y²

13. Answer :

= (-m + 5n)(-m - 5n)

= (-m)² - (5n)²

= m² - 5²n²

= m² - 25n²

14. Answer :

= (-y + 3x)(-y - 3x)

= (-y)² - (3x)²

= y² - 3²x²

= y² - 9x²

15. Answer :

= (a² + b²)(a + b)(a - b)

= (a² + b²)(a² - b²)

= (a²)² - (b²)²

= a⁴ - b⁴

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