Question

Expand ${[\frac{2}{3}x+1]}^3$

Answer 1

$⟶{[\frac{2}{3}x+1]}^3$

Be applying ${(a+b)}^3=a^3+b^3+{3a}^{2}b+{3ab}^2$

We have,

${[\frac{2}{3}x+1]}^3=[{\left(\frac{2}{3}x\right)}^3+{\left(1\right)}^3+3{\left(\frac{2}{3}x\right)}^3\left(1\right)+3\left(\frac{2}{3}x\right)\left(1^2\right)]$

$=[\frac{{8x}^3}{27}+1+\frac{{4x}^3}{3}+2x]$