Solve the following using identities (Part-6)

1. (2 x)^3 + (3 y)^3

Sol. Using the identity

a^3 + b^3 = (a + b) (a^2 + b^2 – ab)

(2 x)^3 + (3 y)^3

(2 x + 3 y) {(2 x)^2 + (3 y)^2 – 2 x * 3 y)

(2 x + 3 y) (4 x^2 + 9 y^2 – 6 x y )

2. (3 x)^3 + (4 y)^3

Sol. Using the identity

a^3 + b^3 = (a + b) (a^2 + b^2 – ab)

(3 x)^3 + (4 y)^3

(3 x + 4 y) {(3 x)^2 + (4 y)^2 – 3 x * 4 y)

(3 x + 4 y) (9 x^2 + 16 y^2 – 12 x y )

3. (x)^3 + (3 y)^3

Sol. Using the identity

a^3 + b^3 = (a + b) (a^2 + b^2 – ab)

(x)^3 + (3 y)^3

(x + 3 y) {(x)^2 + (3 y)^2 – x * 3 y)

(x + 3 y) (x^2 + 9 y^2 – 3 x y )

4. (2 x)^3 + (2 y)^3

Sol. Using the identity

a^3 + b^3 = (a + b) (a^2 + b^2 – ab)

(2 x)^3 + (2 y)^3

(2 x + 2 y) {(2 x)^2 + (2 y)^2 – 2 x * 2 y)

(2 x + 2 y) (4 x^2 + 4 y^2 – 4 x y )

maths-ncert-solution

5. (2 x)^3 - (3 y)^3

Sol. Using the identity

a^3 - b^3 = (a - b) (a^2 - b^2 + ab)

(2 x)^3 - (3 y)^3

(2 x - 3 y) {(2 x)^2 - (3 y)^2 + 2 x * 3 y)

(2 x - 3 y) (4 x^2 - 9 y^2 + 6 x y )

6. (3 x)^3 - (4 y)^3

Sol. Using the identity

a^3 - b^3 = (a - b) (a^2 - b^2 + ab)

(3 x)^3 - (4 y)^3

(3 x - 4 y) {(3 x)^2 - (4 y)^2 + 3 x * 4 y)

(3 x - 4 y) (9 x^2 - 16 y^2 + 12 x y )

7. (x)^3 - (3 y)^3

Sol. Using the identity

a^3 - b^3 = (a - b) (a^2 - b^2 + ab)

(x)^3 - (3 y)^3

(x - 3 y) {(x)^2 - (3 y)^2 + x * 3 y)

(x - 3 y) (x^2 - 9 y^2 + 3 x y )

8. (2 x)^3 - (2 y)^3

Sol. Using the identity

a^3 - b^3 = (a - b) (a^2 - b^2 + ab)

(2 x)^3 - (2 y)^3

(2 x - 2 y) {(2 x)^2 - (2 y)^2 + 2 x * 2 y)}

(2 x - 2 y) (4 x^2 - 4 y^2 + 4 x y )

Milan Tomic

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