Question

1728 -8y^3 is equal to ??

Answer 1

GIVEN :

The expression is $1728-8y^3$

TO FIND :

The simplified form of the given expression.

SOLUTION :

Given expression is $1728-8y^3$

Now solving the given expression as below :

$1728-8y^3$

$=12^3-2^3y^3$

By using the property of exponents :

$a^m.b^m=(ab)^m$

$=12^3-(2y)^3$

By using the Algebraic formula :

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Here a=12 and b=2y and substituting the values in the formula we get,

$=(12-2y)(12^2+12(2y)+(2y)^2)$

$=(12-2y)(144+24y+4y^2)$

$=(12-2y)(4y^2+24y+144)$

$=[2(6-y)][4(y^2+6y+36)]$

$=8(6-y)(y^2+6y+36)$

∴ $1728-8y^3=8(6-y)(y^2+6y+36)$

∴ the simplified form for the given expression is $8(6-y)(y^2+6y+36)$