SOLUTION: Sandy says the product of x2 and x3 +5x2 +1 is x6 +5x4 +x2. Explain the error that Sandy made and give the correct product.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Sandy says the product of x2 and x3 +5x2 +1 is x6 +5x4 +x2. Explain the error that Sandy made and give the correct product.      Log On


   

Question 945696: Sandy says the product of x2 and x3 +5x2 +1 is x6 +5x4 +x2. Explain the error that Sandy made and give the correct product.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the product of x%5E2 and x%5E3+%2B5x%5E2+%2B1 is x%5E6+%2B5x%5E4+%2Bx%5E2:
x%5E2%28x%5E3+%2B5x%5E2+%2B1%29=x%5E6+%2B5x%5E4+%2Bx%5E2
x%5E3%2Ax%5E2+%2B5x%5E2%2Ax%5E2+%2B1%2Ax%5E2=x%5E6+%2B5x%5E4+%2Bx%5E2
x%5E%283%2B2%29+%2B5x%5E%282%2B2%29+%2Bx%5E2=x%5E6+%2B5x%5E4+%2Bx%5E2
x%5E5+%2B5x%5E4+%2Bx%5E2%3C%3Ex%5E6+%2B5x%5E4+%2Bx%5E2
the error that Sandy made was multiplication of x%5E3%2Ax%5E2; she got x%5E6 which is incorrect, should be x%5E5 because she multiplied exponents and broke the first basic exponent rule: Whenever you multiply two terms with the same base, you add the exponents.