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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