Multiplying Monomials

6.2.1 Multiplying Monomials

6.2.1 • Multiplying Monomials

Warm Up

Since monomials are algebraic expressions, we can use the properties of exponents to multiply monomials.

$(3 x^{2}) (- 4 x^{3})$

Compare your answer:

Step 1 - Use the Commutative Property to rearrange the terms.

$3 \cdot (- 4) \cdot x^{2} \cdot x^{3}$

Step 2 - Multiply.

$- 12 x^{5}$

$(\frac{5}{6} x^{3} y) (12 x y^{2})$

Compare your answer:

Step 1 - Use the Commutative Property to rearrange the terms.

$\frac{5}{6} \cdot 12 \cdot x^{3} \cdot x \cdot y \cdot y^{2}$

Step 2 - Multiply.

$10 x^{4} y^{3}$

Multiplying a polynomial by a monomial is done by applying the Distributive Property of Multiplication over Addition.

Find the product of each expression.

$7 x (3 x + 6)$

Compare your answer:

$21 x^{2} + 42 x$

$7 b^{2} (9 b - 4)$

Compare your answer:

$63 b^{3} - 28 b^{2}$

$2 k (5 k^{2} + 3 k - 1)$

Compare your answer:

$10 k^{3} + 6 k^{2} - 2 k$

$4 r^{2} s (2 r^{2} + 8 r s - 12 s^{2})$

Compare your answer:

$8 r^{4} s + 32 r^{3} s^{2} - 48 r^{2} s^{3}$

Building Character: Judgement

A woman with long dark hair wearing an orange shirt shrugs with uncertainty, surrounded by question marks, check marks, crosses, and YES and NO bubbles, conveying confusion or indecision.

A key factor in making sound judgements is not jumping to conclusions. Your judgment will never be perfect, but you can strive to be aware of bias and make corrections when necessary.

Think about yourself. When you face a problem that requires judgment, how many of these things are true?

I independently ask several people for their judgment, and I consider their reasons.
I try to separate my hopes and fears from the facts and beliefs supporting the judgment.

Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!