# 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.

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