Worksheet on Expansion of (a ± b)\(^{2}\) and its Corollaries

Practice the questions given in the worksheet on expansion of (a ± b)\(^{2}\) and its corollaries.

1. Expand the squares of the following:

(i) 4x + y

(ii) 5a + 3b

(iii) 2x + \(\frac{1}{x}\)

2. Expand the following:

(i) (x – 2y)\(^{2}\)

(ii) (3y – 2z)\(^{2}\)

(iii) (3x - \(\frac{1}{3x}\))\(^{2}\)

3. Expand the squares of the following:

(i) \(\frac{3}{2}\) + \(\frac{5}{3}\)n

(ii) 4x - \(\frac{3}{4}\)

(iii) a\(^{2}\) + 1

(iv) a\(^{2}\) - \(\frac{1}{a}\)

4. Simplify:

(i) (3x + 5y)\(^{2}\) + (3x – 5y)\(^{2}\)

(ii) (a - \(\frac{1}{a}\))\(^{2}\) + (a + \(\frac{1}{a}\))\(^{2}\)

(iii) (7x + 4y)\(^{2}\) – (7x – 4y)\(^{2}\)

(iv) (x + \(\frac{1}{x}\))\(^{2}\) – (x - \(\frac{1}{x}\))\(^{2}\)

5. If a + \(\frac{1}{a}\) = 2, find the value of

(i) a\(^{2}\) + \(\frac{1}{a^{2}}\)

(ii) a\(^{4}\) + \(\frac{1}{a^{4}}\)

6. If x - \(\frac{1}{x}\) = 3, find the value of

(i) x\(^{2}\) + \(\frac{1}{x^{2}}\)

(ii) x\(^{4}\) + \(\frac{1}{x^{4}}\)

7. If x + y = 7 and x – y = 3, evaluate

(i) xy

(ii) x\(^{2}\) + y\(^{2}\)

8. If a + b = 8 and ab = 12, find

(i) a\(^{2}\) + b\(^{2}\)

(ii) the difference between a and b.

9. If x\(^{2}\) + 4x – 1 = 0 and x is positive then find the value of

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

(ii) x\(^{2}\) + \(\frac{1}{x^{2}}\)

10. (i) If a + \(\frac{1}{a}\) = 5, find the difference between a and \(\frac{1}{a}\).

(ii) m\(^{2}\) + n\(^{2}\) = 34 and mn = 10\(\frac{1}{2}\), find the value of 2(m + n)\(^{2}\) + (m – n)\(^{2}\).

Answers for the worksheet on expansion of (a ± b)\(^{2}\) and its corollaries are given below.

Answers:

1.(i) 16x\(^{2}\) + 8xy + y\(^{2}\)

(ii) 25a\(^{2}\) + 30ab + 9b\(^{2}\)

(iii) 4x\(^{2}\) + 4 + \(\frac{1}{x^{2}}\)

2. (i) x\(^{2}\) – 4xy + 4y\(^{2}\)

(ii) 9y\(^{2}\) – 12yz + 4z\(^{2}\)

(iii) 9x\(^{2}\) – 2 + \(\frac{1}{9x^{2}}\)

3. (i) \(\frac{9}{4}\) + 5n + \(\frac{25}{9}\)n\(^{2}\)

(ii) 16x\(^{2}\) – 6x + \(\frac{9}{16}\)

(iii) a\(^{4}\) + 2a\(^{2}\) + 1

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

4. (i) 18x\(^{2}\) + 50y\(^{2}\)

(ii) 2a\(^{2}\) + \(\frac{2}{a^{2}}\)

(iii) 112xy

(iv) 4

5. (i) 2

(ii) 2

6. (i) 11

(ii) 119

7. (i) 10

(ii) 29

8. (i) 40

(ii) 4

9. \(\sqrt{20}\)

(ii) 18

10. \(\sqrt{21}\)

(ii) 123

9th Grade Math

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