Question

question give the expansion of (2y + 2z)^3 provide your answer below:

Explanation:

Step1: Recall the binomial - expansion formula

The binomial - expansion formula for \((a + b)^3=a^{3}+3a^{2}b + 3ab^{2}+b^{3}\). Here \(a = 2y\) and \(b = 2z\).

Step2: Calculate \(a^{3}\)

\(a^{3}=(2y)^{3}=2^{3}y^{3}=8y^{3}\).

Step3: Calculate \(3a^{2}b\)

\(3a^{2}b=3\times(2y)^{2}\times(2z)=3\times4y^{2}\times2z = 24y^{2}z\).

Step4: Calculate \(3ab^{2}\)

\(3ab^{2}=3\times(2y)\times(2z)^{2}=3\times2y\times4z^{2}=24yz^{2}\).

Step5: Calculate \(b^{3}\)

\(b^{3}=(2z)^{3}=2^{3}z^{3}=8z^{3}\).

Step6: Combine the terms

\((2y + 2z)^{3}=8y^{3}+24y^{2}z + 24yz^{2}+8z^{3}\).

Answer:

\(8y^{3}+24y^{2}z + 24yz^{2}+8z^{3}\)