Question

( 58 ) 3 using the idenity (a-b)3

Answer 1

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

It’s quite easy actually to find this, if you know basic algebraic expansion. Since (a-b)^3 = (a-b)(a-b)(a-b), you expand one pair first, and then the last a-b.

That being said, it’s useful to memorise basic algebraic identities. This is a list of a few easy ones:

Answer 2

$(58) {}^{3}$
$= > (60 - 2) {}^{3}$
$= > 60 {}^{3} -2 {}^{3} - 3 \times 60 {}^{2} \times 2 + 3 \times 60 \times 2 {?}^{2}$
$= > 216000 - 8 - 6 \times 3600 + 180 \times 4$
$= > 216000 - 8 - 21600 + 720$
$= > 216720 - 21608$
$= > 195112$