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Monomial Times Polynomial

Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 47 of 64.

The distributive property from Fundamentals, a(b + c) = ab + ac, never asked its multiplier to be a plain number. 3x(x - 4) distributes exactly the same way: the 3x multiplies each term inside.

Each little product is a product-rule job: 3x * x = 3x^2 and 3x * (-4) = -12x. So 3x(x - 4) = 3x^2 - 12x.

Two old skills, one new reach: distribute to every term, and multiply each pair by "numbers multiply, exponents add". Everything this chapter does is built from those two moves.

Challenge

Medium

Expand 4x(x - 2).

Try it yourself

4x(x - 2)

Simplify the expression

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Exponents & Polynomials

1What a Power Is

Repeated Multiplication Squares and Cubes Powers of Negative Numbers Where the Minus Lives Recap: First Powers

4Power of a Power

A Power Raised Again Why Exponents Multiply Product Rule or Power Rule?The Rule in Letters Recap: Power of a Power

7Scientific Notation

Very Large Numbers Back to Standard Form More Practice, Bigger Numbers Very Small Numbers Multiplying the Notation Recap: Scientific Notation

10Multiplying Polynomials

Monomial Times PolynomialMinding the Signs Binomial Times Binomial With Coefficients The Square of a Binomial A Difference of Squares Recap: Multiplying

2The Product Rule

Multiplying Same Bases With Coefficients More Than Two Factors The Rule in Letters Recap: The Product Rule

5Product and Quotient Powers

Every Factor Gets the Power With a Number Inside A Power of a Quotient All Three Rules Together Recap: Products and Quotients

8What a Polynomial Is

Terms with Powers The Degree Like Terms, Only Stronger Recap: Meet the Polynomials

11Dividing by a Monomial

Splitting the Fraction Dividing by a Variable Term Bigger Splits Cancel with Care Recap: Dividing