Simplify (x−2y)
3
−6xy(x−2y).
- Ax
3
−8y
3
−12x
2
y+24xy
2 - Bx
3
−8y
3
+12x
2
y−24xy
2 - Cx
3
−8y
3 - Dx
3
−8x
2
y+16xy
2
−8y
3
Solution & Step-by-step Explanation
The given expression is:
E=(x−2y)
3
−6xy(x−2y)
Let's expand using the standard algebraic identity:
(a−b)
3
=a
3
−b
3
−3ab(a−b)
Here, let a=x and b=2y.
(x−2y)
3
=x
3
−(2y)
3
−3(x)(2y)(x−2y)
(x−2y)
3
=x
3
−8y
3
−6xy(x−2y)
Substitute this back into the original expression:
E=[x
3
−8y
3
−6xy(x−2y)]−6xy(x−2y)
E=x
3
−8y
3
−12xy(x−2y)
E=x
3
−8y
3
−12x
2
y+24xy
2
Thus, the simplified expression matches option A.
E=(x−2y)
3
−6xy(x−2y)
Let's expand using the standard algebraic identity:
(a−b)
3
=a
3
−b
3
−3ab(a−b)
Here, let a=x and b=2y.
(x−2y)
3
=x
3
−(2y)
3
−3(x)(2y)(x−2y)
(x−2y)
3
=x
3
−8y
3
−6xy(x−2y)
Substitute this back into the original expression:
E=[x
3
−8y
3
−6xy(x−2y)]−6xy(x−2y)
E=x
3
−8y
3
−12xy(x−2y)
E=x
3
−8y
3
−12x
2
y+24xy
2
Thus, the simplified expression matches option A.