Question

grab a piece of lined paper from the round table, then sit down in your seat and solve the following problem on the lined paper as your do now: $2x(8x^3 + 4x^2)$

Explanation:

Step1: Apply distributive property

To expand \(2x(8x^{3}+4x^{2})\), we use the distributive property \(a(b + c)=ab+ac\), where \(a = 2x\), \(b=8x^{3}\) and \(c = 4x^{2}\).
So we get \(2x\times8x^{3}+2x\times4x^{2}\)

Step2: Multiply the coefficients and add the exponents of like bases

For \(2x\times8x^{3}\), multiply the coefficients \(2\times8 = 16\) and add the exponents of \(x\) (using the rule \(x^{m}\times x^{n}=x^{m + n}\)): \(x\times x^{3}=x^{1+3}=x^{4}\), so \(2x\times8x^{3}=16x^{4}\)
For \(2x\times4x^{2}\), multiply the coefficients \(2\times4=8\) and add the exponents of \(x\): \(x\times x^{2}=x^{1 + 2}=x^{3}\), so \(2x\times4x^{2}=8x^{3}\)

Step3: Combine the terms

Combining the two terms from step 2, we have \(16x^{4}+8x^{3}\)

Answer:

\(16x^{4}+8x^{3}\)