factorise : 6( x- y)2 - x + y - 15. (step by step explanation please)
Answers
Answer:
The expression is 6(x-y)^2-x+y-156(x−y)
2
−x+y−15 and factorise it.
TO FACTORISE :
The given expression is 6(x-y)^2-x+y-156(x−y)
2
−x+y−15
SOLUTION :
Given that the expression is 6(x-y)^2-x+y-156(x−y)
2
−x+y−15
First factorising the given expression we have that,
That is now solving the given expression as below:
6(x-y)^2-x+y-156(x−y)
2
−x+y−15
By using the algebraic identity :
(a-b)^2=a^2-2ab+b^2(a−b)
2
=a
2
−2ab+b
2
=6(x^2-2xy+y^2)-x+y-15=6(x
2
−2xy+y
2
)−x+y−15
By using the Distributive property :
a(x+y+z)=ax+ay+az
=6(x^2)+6(-2xy)+6(y^2)-x+y-15=6(x
2
)+6(−2xy)+6(y
2
)−x+y−15
=6x^2-12xy+ 6y2-x + y - 15=6x
2
−12xy+6y2−x+y−15
=6x(x-2y)-(x+15)+y(6y+1)=6x(x−2y)−(x+15)+y(6y+1)
∴ 6(x-y)^2-x+y-15=6x(x-2y)-(x+15)+y(6y+1)6(x−y)
2
−x+y−15=6x(x−2y)−(x+15)+y(6y+1)
∴ These groups have no common factor.