factorise 2x minus 3 whole square minus 32
Answers
Step-by-step explanation:
GIVEN :
The expression is 2(x-3)^2-322(x−3)
2
−32
TO FIND :
The factorised polynomial for the given expression.
SOLUTION :
Given expression is 2(x-3)^2-322(x−3)
2
−32
Now factorise the given expression as below :
2(x-3)^2-322(x−3)
2
−32
By using the algebraic formula:
(a-b)^2=a^2-2ab+b^2(a−b)
2
=a
2
−2ab+b
2
=2(x^2-2(x)(3)+3^2)-32=2(x
2
−2(x)(3)+3
2
)−32
=2(x^2-6x+9)-32=2(x
2
−6x+9)−32
By using the Distributive property :
a(x+y+z)=ax+ay+az
=2(x^2)+2(-6x)+2(9)-32=2(x
2
)+2(−6x)+2(9)−32
=2x^2-12x+18-32=2x
2
−12x+18−32
By adding the like terms
=2x^2-12x-14=2x
2
−12x−14
Dividing by 2 we get
=x^2-6x-7=x
2
−6x−7
=(x+1)(x-7)=(x+1)(x−7)
2(x-3)^2=(x+1)(x-7)2(x−3)
2
=(x+1)(x−7)
∴ the factorised expression to the given expression 2(x-3)^22(x−3)
2
is (x-1)(x+7)
∴ 2(x-3)^2=(x+1)(x-7)2(x−3)
2
=(x+1)(x−7)
Answer:
if it is wrote like it OK
