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
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