Sandy says the product of x^2 and x^3+5x^2+1 is x^6+5x^4+x^2. Explain the error that Sandy made and give the correct product.

Question

x^2 times x^3+5x^2+1 is not x^6+5x^4+x^2 what did Sandy do wrong and what is the correct answer?

Answer 1

The error she made was a distribution one.  She did not distribute the x² with the x³ correctly.  Since the bases are the same, she needs to add the exponents.  What she did was multiply them, and got a term of x⁶ as the first term in the product, when it should be x⁵.  Everything else is OK. 

 

So the correct full product is

 

x²(x³ + 5x² + 1) =

 

x⁵ + 5x⁴ + x²