Introduction to Algebraic Identities

Q. Expand $\left(3a+\frac{2}{b}\right)\left(2a-\frac{3}{b}\right)$

1. $6a^2+\frac{5a}{b}-\frac{6}{b^2}$
2. $6a^2-\frac{5a}{b}-\frac{6}{b^2}$
3. $6a^2+\frac{5a}{b}+\frac{6}{b^2}$
4. $6a^2-\frac{5a}{b}+\frac{6}{b^2}$

Q. Expand $\left(2x-\frac{1}{x}\right)\left(3x+\frac{2}{x}\right)$

1. $6x^2-1-\frac{2}{x^2}$
2. $6x^2-1+\frac{2}{x^2}$
3. $6x^2+1+\frac{2}{x^2}$
4. $6x^2+1-\frac{2}{x^2}$

Q. In the expansion of $(5x-3)(x+2{)}^2$ ; find the constant term .

1. 8
2. -12
3. 5
4. 17

Q. The sum of two numbers is 9 and their product is 20. Find the sum of their cubes.

1. 1269
2. 79
3. 190
4. 189

Q. Expand $(5x-3y+2)(5x+3y+2)$

1. $25x^2+20x+4-9y^2$
2. $25x^2-20x-4-9y^2$
3. $16x^2+20x+4-9y^2$
4. $16x^2+25x+4-9y^2$

Q. In the expansion of $(5x-3)(x+2{)}^2$ ; find the coefficient of $x$.

1. 5
2. -12
3. 8
4. 20

Q. Which of the following can be solved using algebraic identities?

1. $4+6$
2. $(5+3{)}^2$
3. $(15-10{)}^2$
4. $12-4$
5. $4^2-3^2$
6. $6-4\times 6+4$
7. $6+3\times 6+4$
8. $5-2\times 7+3$

Q. $(a+b{)}^2$ expands as $a^2+b^2+2ab$.

1. True
2. False

Q. Find the value of ${4.9}^2$ using a suitable algebraic identity.

1. 24.01

Q. All equations are identities but all identities may not be equations.

1. True
2. False