Question

factorise by using suitable identities in the following questions a. (42)^3-(18)^3-(24)^3​

Answer 1

Step-by-step explanation:

The given expression (42)

3

−(18)

3

−(24)

3

can be rewritten as .

We know that one of the identity is x

x³+y³+z³−3xyz=(x+y+z)(x³+y³+z³−xy−yz−zx)

We first find x+y+z by substituting x=42,y=−18,z=−24 as follows:

x+y+z=42−18−24=0

Therefore, the above identity becomes:

x³+y³+z³−3xyz=0×(x²+y²+z²−xy−yz−zx)

⇒x³+y³+z³−3xyz=0

⇒(42)³+(−18)³+(−24)³−3(42×−18×−24)=0

⇒(42)³+(−18)³+(−24)³=3×18144

⇒(42)³−(18)³−(24)³=54432

Hence, (42)³ −(18)³ −(24)³ =54432.