Question

(b)

(i) Factorise 1000x³-y³ completely.

(ii) Hence, without using a calculator, show that 124 is a factor of 992.

Answer 1

i. (10-y)(100x^2 +10xy + y^2)

ii. See the explanation

Explanation:

i. 1000x³-y³ =

10³x³ - y³ =

(10x)³ - y³ = ==> use formula: x³ - y³ = (x-y)(x^2+yx+y^2)

(10-y)((10x)^2 +10xy + y^2) =

(10-y)(10^2 * x^2 +10xy + y^2) = ==> simplify

(10-y)(100x^2 +10xy + y^2)

ii. 992/124=

(992-192)/(124-24)=

800/100 = 8

As a result, 8*124=992.

Hence, 124 (and 8) is a factor of 992