Question

How do you simplify \[{\left( {4x - 3} \right)^3}\] ?

Answer 1

Hint: This is an identity and expansion based question. We will use cubic identity expansion here. Just we will replace the values of a and b by the terms \[4x\] and 3. That is the way to solve the problem. Also take care of the sign in the middle of the terms and use the expansion formula wisely.

Formula used:\[{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\]

Complete step-by-step solution:
We know that \[{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\] is the cubic identity. We will use the same for simplifying the cube above.
\[{\left( {4x - 3} \right)^3} = {\left( {4x} \right)^3} - 3 \times {\left( {4x} \right)^2} \times 3 + 3 \times 4x \times {3^2} - {3^3}\]
Now taking the cubes and squares we get,
\[{\left( {4x - 3} \right)^3} = 64{x^3} - 3 \times 16{x^2} \times 3 + 3 \times 4x \times 9 - 27\]
On taking the product we get,
\[{\left( {4x - 3} \right)^3} = 64{x^3} - 144{x^2} + 108x - 27\]
This is the correct and simplified answer because there are all different terms.

Thus the correct answer is $64{x^3} - 144{x^2} + 108x - 27$

Note: Here note that we just have to expand the bracket and not to put any value of x. Also note that in other expansions or equations if we come across any similar terms that are terms having the same coefficient then perform necessary operations mentioned in the question and then finish the answer.