Multiply the polynomials using the special product formulas. (3x-2)^{3}

Multiply the polynomials using the special product formulas.
${\left(3x-2\right)}^{3}$
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Step 1
Multiply the polynomials using the special product formulas.
${\left(3x-2\right)}^{2}$
Step 2
Now, ${\left(3x-2\right)}^{3}$
$={\left(3x\right)}^{3}-3\cdot {\left(3x\right)}^{2}+3\cdot 3x\cdot {2}^{2}-{2}^{3}$
$\left(\because {\left(a-b\right)}^{3}={a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}\right)$
$=27{x}^{3}-3\left(9{x}^{2}\right)\cdot 2+9x\cdot 4-8$
$=27{x}^{3}-54{x}^{2}+36x-8$
$\therefore {\left(3x-2\right)}^{3}=27{x}^{3}-54{x}^{2}+36x-8$