Question

Expand the expression:
(3a - 2b)^3

Show complete computation.​

Answer 1

`27a^3-54a^2b+36ab^2-8b^3`

Explanation:

To expand the expression (3a - 2b)³, we can use the Perfect Cube Formula.

`\boxed{\begin{minipage}{6 cm}\underline{Perfect Cube Formula}\\\\$(x-y)^3=x^3-3x^2y+3xy^2-y^3$\\\end{minipage}}`

Let:

• x = 3a
• y = 2b

Substitute the values into the formula, and use the exponent rule

`\boxed{(xy)^n=x^n \cdot y^n}` :

Therefore:

`\begin{aligned}(3a-2b)^3&=(3a)^3-3(3a)^2(2b)+3(3a)(2b)^2-(2b)^3\\&=3^3 \cdot a^3-3 \cdot 3^2 \cdot a^2 \cdot 2b+3 \cdot 3a \cdot 2^2\cdot b^2-2^3\cdot b^3\\&=27a^3-3 \cdot 9 \cdot a^2 \cdot 2b+9a \cdot 4b^2-8b^3\\&=27a^3-54a^2b+36ab^2-8b^3\end{aligned}`

So the expression (3a - 2b)³ expanded is 27a³ - 54a²b + 36ab² - 8b³.

Answer 2

I have solved it and attached in the explanation.

Explanation: