Question

Q.1 Factor the following using identities wherever necessary
1) x to the power 2- 9
3) x to the power 2 - 8x + 16
4) 2x to the power 2 -14x
5) 20a square b - 25a3b
6) a square + ac + ab + bc
7) 15xy – 6x + 5y – 2
8) 3x + 9y
9) 3xyz + 27
10) 2abc + 7ac + 9bc

Answer 1

Step-by-step explanation:

1.

${x}^{2} - 9 \\ = {x}^{2} - {3}^{2} \\ = (x + 3)(x - 3)$

2.

${x}^{2} - 8x + 16 \\ = {x}^{2} - 2 \times x \times 4 + {4}^{2} \\ = {(x - 4)}^{2} \\ = (x - 4)(x - 4)$

3.

${(2x)}^{2} - 14x \\ = 4 {x}^{2} - 14x \\ = 2x(2x - 7)$

4.

$20 {a}^{2} b - 25 {a}^{3} b \\ = 5 {a}^{2} b(4 - 5a)$

6.

${a}^{2} + ac + ab + bc \\ = a(a + c) + b(a + c) \\ = (a + c)(a + b)$

7.

$15xy - 6x + 5y - 2 \\ =$

8.

$3x + 9y \\ = 3(x + 3y)$

9.

$3xyz + 27 \\ = 3(xyz + 9)$

10.

$2abc + 7ac + 9bc \\ = 9bc + 9abc - 7abc + 7ac \\ = 9bc(1 + a) - 7ac(b - 1)$

something went wrong in question number 7 and 10.

and questions number 2 is missing.