factorize:
64x - 729y
Answers
Answer:
64x^6-729y^6=(8x^3+27y^3)(2x-3y)(4x^2+6xy+9y^2)64x
6
−729y
6
=(8x
3
+27y
3
)(2x−3y)(4x
2
+6xy+9y
2
)
Step-by-step explanation:
Given : Expression 64x^6-729y^664x
6
−729y
6
To find : Factories the expression ?
Solution :
The expression is written as,
64x^6-729y^6=(8x^3)^2-(27y^3)^264x
6
−729y
6
=(8x
3
)
2
−(27y
3
)
2
Applying a^2-b^2=(a+b)(a-b)a
2
−b
2
=(a+b)(a−b)
64x^6-729y^6=(8x^3+27y^3)(8x^3-27y^3)64x
6
−729y
6
=(8x
3
+27y
3
)(8x
3
−27y
3
)
64x^6-729y^6=(8x^3+27y^3)((2x)^3-(3y)^3)64x
6
−729y
6
=(8x
3
+27y
3
)((2x)
3
−(3y)
3
)
Applying identity, a^3-b^3=(a-b)(a^2+ab+b^2)a
3
−b
3
=(a−b)(a
2
+ab+b
2
)
64x^6-729y^6=(8x^3+27y^3)(2x-3y)((2x)^2+(2x)(3y)+(3y)^2)64x
6
−729y
6
=(8x
3
+27y
3
)(2x−3y)((2x)
2
+(2x)(3y)+(3y)
2
)
64x^6-729y^6=(8x^3+27y^3)(2x-3y)(4x^2+6xy+9y^2)64x
6
−729y
6
=(8x
3
+27y
3
)(2x−3y)(4x
2
+6xy+9y
2
)
Therefore, the factories form is 64x^6-729y^6=(8x^3+27y^3)(2x-3y)(4x^2+6xy+9y^2)64x
6
−729y
6
=(8x
3
+27y
3
)(2x−3y)(4x
2
+6xy+9y
2
)