DAV Class 7 Maths Chapter 6 Worksheet 6

by

Factorise the following expressions.

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

Solution:

\begin{align*} (x + y)(2x + 3y) - (x + y)(x + 1) \\ \end{align*}

\begin{align*} &= (x + y)(2x + 3y) - (x + y)(x + 1) \\ &= (x + y) \left[ (2x + 3y) - (x + 1) \right] \\ &= (x + y) \left[ 2x + 3y - x - 1 \right] \\ &= (x + y) \left[ x + 3y - 1 \right] \\ \end{align*}

2. 9x(6x - 5y)- 12x2(6x - 5y)

Solution:

\begin{align*} 9x(6x - 5y) - 12x^2(6x - 5y) \\ \end{align*}

\begin{align*} &= 9x(6x - 5y) - 12x^2(6x - 5y) \\ &= (6x - 5y) (9x - 12x^2) \\ &= (6x - 5y)3x(3 - 4x) \\ &= 3x(6x - 5y)(3 - 4x) \\ \end{align*}

3. x3(a - 2b) + x2(a - 2b)

Solution:

\begin{align*} x^3(a - 2b) + x^2(a - 2b) \\ \end{align*}

\begin{align*} &= x^3(a - 2b) + x^2(a - 2b) \\ &= (a - 2b)(x^3 + x^2) \\ &= (a - 2b)x^2(x + 1) \\ &= x^2(a - 2b)(x + 1) \\ \end{align*}

4. (a - b)2 + (a - b)

Solution:

\begin{align*} (a - b)^2 + (a - b) \\ \end{align*}

\begin{align*} &= (a - b)^2 + (a - b) \\ &= (a - b)[(a - b) + 1] \\ &= (a - b)(a - b + 1) \end{align*}

5. 3a(p - 2q) - b(p - 2q)

Solution:

\begin{align*} 3a(p - 2q) - b(p - 2q) \\ \end{align*}

\begin{align*} &= 3a(p - 2q) - b(p - 2q) \\ &= (p - 2q)(3a - b) \\ \end{align*}

6. 8(5x + 9y) + 12(5x + 9y)

Solution:

\begin{align*} 8(5x + 9y) + 12(5x + 9y) \\ \end{align*}

\begin{align*} &= 8(5x + 9y) + 12(5x + 9y) \\ &= (5x + 9y)(8 + 12) \\ &= (5x + 9y)(20) \\ &= 20(5x + 9y) \end{align*}

7. 1 + x + xy + x2y

Solution:

\begin{align*} 1 + x + xy + x^2y \\ \end{align*}

\begin{align*} &= 1 + x + xy + x^2y \\ &= 1(1 + x) + xy(1 + x ) \\ &= (1 + x) (1 + xy) \end{align*}

8. x2 + xy + xz +yz

Solution:

\begin{align*} x^2 + xy + xz + yz \\ \end{align*}

\begin{align*} &= x^2 + xy + xz + yz \\ &= x(x + y) + z(x + y) \\ &= (x + y)(x + z) \end{align*}

9. a(a + b) + 8a + 8b

Solution:

\begin{align*} a(a + b) + 8a + 8b \\ \end{align*}

\begin{align*} &= a(a + b) + 8a + 8b \\ &= a(a + b) + 8(a + b) \\ &= (a + 8)(a + b) \end{align*}

10. a2 + bc + ac + ab

Solution:

\begin{align*} a^2 + bc + ac + ab \\ \end{align*}

\begin{align*} &= a^2 + ac + ab + bc \\ &= a(a + c) + b(a + c) \\ &= (a + c)(a + b) \end{align*}

11. a2 + 2a + ab + 2b

Solution:

\begin{align*} a^2 + 2a + ab + 2b \\ \end{align*}

\begin{align*} &= a^2 + 2a + ab + 2b \\ &= a(a + 2) + b(a + 2) \\ &= (a + 2)(a + b) \end{align*}

12. ax + ay - bx -by

Solution:

\begin{align*} ax + ay - bx - by \\ \end{align*}

\begin{align*} &= ax + ay - bx - by \\ &= a(x + y) - b(x + y) \\ &= (x + y)(a - b) \end{align*}