factorize 8(x+y)³-27(x-y)³
Answers
Step-by-step explanation:
x+5y)(19x
2
−10xy+7y
2
) is the value of \bold{8(x+y)^3-27(x-y)^3}8(x+y)
3
−27(x−y)
3
Given:
8(x+y)^3-27(x-y)^38(x+y)
3
−27(x−y)
3
To find:
The value of 8(x+y)^3-27(x-y)^3=?8(x+y)
3
−27(x−y)
3
=?
Solution:
Given is 8(x+y)^3-27(x-y)^38(x+y)
3
−27(x−y)
3
Observing the given it is found that using the algebraic identity it can be expressed
The algebraic identity
\bold{(a^3-b^3 )=(a-b)(a^2+ab+b^2)}(a
3
−b
3
)=(a−b)(a
2
+ab+b
2
)
From the given a=2(x+y) ,b=3(x-y)
Substituting in the formula we get
(2(x+y))^3-(3(x-y))^3(2(x+y))
3
−(3(x−y))
3
=(2(x+y)-3(x-y)) 〖[(2(x+y))〗^2+2(x+y)3(x-y)+(3(x-y))^2]=(2(x+y)−3(x−y))〖[(2(x+y))〗
2
+2(x+y)3(x−y)+(3(x−y))
2
]
Elaborating the terms using the formula and cancelling out
=(2x+2y+3x-3y)[4x^2+8xy+4y^2+6x^2-6xy+6xy-6y^2+9x^2-18xy+9y^2 ]=(2x+2y+3x−3y)[4x
2
+8xy+4y
2
+6x
2
−6xy+6xy−6y
2
+9x
2
−18xy+9y
2
]
Simplifying the terms, we get
=(-x+5y)(19x^2-10xy+7y^2)=(−x+5y)(19x
2
−10xy+7y
2
)
Therefore, the value of \bold{8(x+y)^3-27(x-y)^3 is (-x+5y)(19x^2-10xy+7y^2)}8(x+y)
3
−27(x−y)
3
is(−x+5y)(19x
2
−10xy+7y
2
)