Algebra 1 : How to multiply a monomial by a polynomial

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #21 : Monomials

Simplify:

Possible Answers:

The answers provided do not show the correct simplificaiton. 

Correct answer:

Explanation:

When multiplying a whole number by a polynomial, we simply multiply that number by whatever coefficient is present in front of the variables of the polynomial. We then maintain the variables in the simplified expression.

Example Question #21 : Monomials

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Use the distributive property to multiply the monomial and polynomial.

Example Question #22 : Monomials

Evaluate the expression:

Possible Answers:

Correct answer:

Explanation:

Multipying a monomial and trinomial boils down to distributing the monomial amongst all the parts of the trinomial as such:

After some cleanup we get:

Example Question #21 : How To Multiply A Monomial By A Polynomial

Multiply:

Possible Answers:

Correct answer:

Explanation:

All we need to do here is multiply every term within the polynomial  by the monomial on the outside of the parentheses: .

To do this we need to multiply every term by  and by . Remember that when we multiply by a variable (in this case ), we need to add  to each of the exponents.

So this leaves us with .

Example Question #23 : Monomials

Divide:  

Possible Answers:

Correct answer:

Explanation:

To divide this, we must pull out a common factor from the numerator and denominator.

The common factor from the numerator is only .

The common factor from the denominator is .

The only term that will cancel is the .  We cannot cancel the  inside  and  terms because they are different entities of a quantity.

The answer is:  

Example Question #21 : How To Multiply A Monomial By A Polynomial

Which of the following is equivalent to the given statement?

Possible Answers:

Correct answer:

Explanation:

Which of the following is equivalent to the given statement?

This question asks us to distribute a monomial through a polynomial. To do so, we need to multiply the monomial (4b) by each part of the polynomial in parentheses.

So our answer in standard form is as follows:

Example Question #21 : How To Multiply A Monomial By A Polynomial

Multiply the polynomial by the monomial.

Possible Answers:

Correct answer:

Explanation:

When multiplying a polynomial and a monomial, distribute the monomial into the polynomial:

Then simplify and the answer is: 

Example Question #24 : Monomials

Multiply the polynomial by the monomial.

Possible Answers:

Correct answer:

Explanation:

When multiplying a polynomial and a monomial, distribute the monomial into the polynomial:

Then simplify and the answer is: 

Example Question #25 : Monomials

Multiply the polynomial by the monomial.

 

 
Possible Answers:

Correct answer:

Explanation:

When multiplying a polynomial and a monomial, distribute the monomial into the polynomial:

Then simplify and the answer is: 

Example Question #21 : Monomials

Multiply:  

Possible Answers:

Correct answer:

Explanation:

Distribute the  term through every term inside the parentheses.

Simplify and multiply out each term.

The answer is:  

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