(x+2)^3 = 2x(x^2 1) ∴ (a+b)^3 = a^3+b^3+3a^2b+3ab^2 x^3+8+3× x^2× 2+3× x× 2^2 = 2x^3 2x x^3+8+6x^2+3× 4× x = 2x^3 2x x^3+8+6x^2+12x 2x^ ...

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Algebraic Identities

Solve: x+23=...

Question

Solve: $(x + 2)^{3} = 2 x (x^{2} - 1)$

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Solution

$(x + 2)^{3} = 2 x (x^{2} - 1)$
$∴ (a + b)^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$
$x^{3} + 8 + 3 \times x^{2} \times 2 + 3 \times x \times 2^{2} = 2 x^{3} - 2 x$
$x^{3} + 8 + 6 x^{2} + 3 \times 4 \times x = 2 x^{3} - 2 x$
$x^{3} + 8 + 6 x^{2} + 12 x - 2 x^{3} + 2 x = 0$
$- x^{3} + 6 x^{2} + 14 x + 8 = 0$

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