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