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Information about 8 1 Multiplying Monomials

Published on January 7, 2008

Author: kdwilliams

Source: slideshare.net

algebra 1 intro to monomials

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What is a MONOMIAL? A monomial can be defined as: a number (by itself, known as a constant) a variable, or the product of a number and a variable ( any expression involving the DIVISION of variables is NOT a monomial!)

A monomial can be defined as:

a number (by itself, known as a constant)

a variable, or

the product of a number and a variable

( any expression involving the DIVISION of variables is NOT a monomial!)

Determine if the following are monomials: -3x 2 y 11 3m + 4n xyz 4h / 3j

-3x 2 y

11

3m + 4n

xyz

4h / 3j

The parts of a monomial coefficient 3m² exponent base

coefficient

3m² exponent

base

Product of POWERS To multiply two powers that have the same base, ADD the exponents: m ² • m³ = m 5 To multiply two monomials that have the same base, with coefficients: multiply BIG, add LITTLE: ( 5x )( 2x ² ) = 10x ³ *Don’t forget that variables without an exponent are understood to have a power of 1!!

To multiply two powers that have the same base, ADD the exponents:

m ² • m³ = m 5

To multiply two monomials that have the same base, with coefficients: multiply BIG, add LITTLE:

( 5x )( 2x ² ) = 10x ³

*Don’t forget that variables without an exponent are understood to have a power of 1!!

Let’s try something harder! How about this one?

How about this one?

DON’T PANIC!! JUST FOLLOW THE RULES AND GO ONE STEP AT A TIME! FIRST, MULTIPLY ALL OF THE COEFFICIENTS TOGETHER: - 5 · 3 · 2/5 = - 6 THEN, ADD UP THE EXPONENTS ON THE VARIABLES: THERE ARE X’S AND Y’S TO COUNT UP: HOW MANY X’S ARE THERE? HOW MANY Y’S ARE THERE? YOU SHOULD GET: x 5 y 6 SQUASH THEM TOGETHER, AND YOUR ANSWER IS -6 x 5 y 6

JUST FOLLOW THE RULES AND GO ONE STEP AT A TIME!

FIRST, MULTIPLY ALL OF THE COEFFICIENTS TOGETHER:

- 5 · 3 · 2/5 = - 6

THEN, ADD UP THE EXPONENTS ON THE VARIABLES:

THERE ARE X’S AND Y’S TO COUNT UP: HOW MANY X’S ARE THERE? HOW MANY Y’S ARE THERE?

YOU SHOULD GET: x 5 y 6

SQUASH THEM TOGETHER, AND YOUR ANSWER IS -6 x 5 y 6

Power of a Power To raise a power to a power, you MULTIPLY the exponents: (x ³)² = x 6 If there is a constant involved, don’t forget to raise it to the power as well! (2m²) 4 = 16m 8

To raise a power to a power,

you MULTIPLY the exponents:

(x ³)² = x 6

If there is a constant involved,

don’t forget to raise it to the power as well!

(2m²) 4 = 16m 8

Power of a Product: Raise each factor to that same power (2x 3 y 4 ) 5 = 32x 15 y 20 (now that’s POWERFUL!)

Raise each factor to that same power

(2x 3 y 4 ) 5 = 32x 15 y 20

(now that’s POWERFUL!)

Putting it all together: Simplify the following, using the rules we have just covered: 2 x 5 y 4 (2 x 3 y 6 ) 5 (4 x 2 y ) (2 xy 2 z 3 ) 3

Simplify the following,

using the rules we have just covered:

2 x 5 y 4 (2 x 3 y 6 ) 5

(4 x 2 y ) (2 xy 2 z 3 ) 3

Applications GEOMETRY: Express the area of this circle as a monomial. Area = π r 2 (Formula for the area of a circle)

GEOMETRY: Express the area

of this circle as a monomial.

Area = π r 2 (Formula for the area of a circle)

More applications Find the volume of the rectangular solid: Volume of a rectangular solid: l •w•h

Find the volume of the rectangular solid:

Volume of a rectangular solid: l •w•h

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