Question

Q.(1)
(a) Factorize: x²+5x-14 and x6-y6​

Answer 1

Step-by-step explanation:

Given:-

x²+5x-14 and x6-y6

To find :-

Factorize: x²+5x-14 and x⁶-y⁶

Solution:-

1) Given expression is x²+5x-14

=>x²-2x+7x-14

=>x(x-2)+7(x-2)

=>(x-2)(x+7)

x²+5x-14 = (x-2)(x+7)

2)Given expression is x⁶-y⁶

=>(x³)²-(y³)²

This is in the form of a²-b²

Here, a=x³ and b=y³

a²-b²=(a+b)(a-b)

=>(x³+y³)(x³-y³)

since a³+b³=(a+b)(a²-ab+b²)

a³-b³=(a-b)(a²+ab+b²)

=>(x+y)(x²-xy+y²)(x-y)(x²+xy+y²)

=>(x+y)(x-y)(x²+xy+y²)(x²-xy+y²)

x⁶-y⁶=(x+y)(x-y)(x²+xy+y²)(x²-xy+y²)

Answer:-

1)x²+5x-14 = (x-2)(x+7)

2)x⁶-y⁶=(x+y)(x-y)(x²+xy+y²)(x²-xy+y²)