Question

please solve this (x+2)^3 + (x-2)^3​

Answer 1

Solution :-

Given that

(x+2)³+(x-2)³

We know that

(a+b)³ = a³+3a²b+3ab²+b³

(a-b)³ = a³-3a²b+3ab²-b³

Where, a = x and b = 2

(x+2)³+(x-2)³

= [x³+3x²(2)+3(x)(2²)+2³]+[x³-3x²(2)+3(x)(2²)-2³]

= [x³+6x²+12x+8]+[x³-6x²+12x-8]

= x³+6x²+12x+8+x³-6x²+12x-8

= (x³+x³)+(6x²-6x²)+(12x+12x)+(8-8)

= 2x³+0+24x+0

= 2x³+24

Alternative Method:-

Given that

(x+2)³+(x-2)³

It is in the form of (a+b)³+(a-b)³

Where a = x and b = 2

We know that

(a+b)³+(a-b)³ = 2a³+6ab²

(x+2)³+(x-2)³

= 2(x)³+6(x)(2)²

= 2x³+6x(4)

= 2x³+24x

Answer :-

(x+2)³+(x-2)³ = 2x³+24x

Used formulae:-

• (a+b)³ = a³+3a²b+3ab²+b³

• (a-b)³ = a³-3a²b+3ab²-b³

• (a+b)³+(a-b)³ = 2a³+6ab²