Worksheet on Simplification of (a + b)(a – b) | Hint Practice the questions
given in the worksheet on simplification of (a + b)(a – b).

1. Simplify by applying standard formula.

(i) (5x – 9)(5x + 9)

(ii) (2x + 3y)(2x – 3y)

(iii) (a + b – c)(a – b + c)

(iv) (x + y – 3)(x + y + 3)

(v) (1 + a)(1 – a)(1 + a^2)

(vi) (a + (frac{2}{a}) – 1)(a – (frac{2}{a}) – 1)

2. If a – (frac{1}{a}) = 3, find the value of a(^{2}) – (frac{1}{a^{2}}).

3. If x – (frac{1}{x}) = (frac{3}{2}), find the value of

(i) x + (frac{1}{x})

(ii) x(^{2}) + (frac{1}{x^{2}})

(iii) x(^{2}) – (frac{1}{x^{2}})

(iv) x(^{4}) + (frac{1}{x^{4}})

(v) x(^{4}) – (frac{1}{x^{4}})

4. (i) Simplify: (1 – x)(1 + x)(1 + x(^{2}))(1 + x(^{4})).

(ii)Express: (x(^{2}) + 5x + 12)(x(^{2}) – 5x + 12) as a difference of two squares.

(iii) If (frac{a}{b}) = (frac{b}{c}), prove that (a + b + c)(a – b + c) = a(^{2}) + b(^{2}) + c(^{2}).

Answers for the worksheet on simplification of (a + b)(a – b) are given below.

1. (i) 25x(^{2}) – 81

(ii) 4x(^{2}) – 9y(^{2})

(iii) a(^{2}) – b(^{2}) – c(^{2}) + 2bc

(iv) x(^{2}) + 2xy + y(^{2}) – 9

(v) 1 – a(^{4})

(vi) a(^{2}) – 2a + 1 – (frac{4}{a^{2}})

2. ± 3(sqrt{3})

3. (i) ±(frac{5}{2})

(ii) (frac{17}{4})

(iii) ±(frac{15}{4})

(iv) (frac{257}{16})

(v) ±(frac{255}{16})

4. (i) 1 – x(^{8})

(ii) (x(^{2}) + 12)(^{2}) – (5x)(^{2})

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