Download Multiplying Monomials

Chapter 8.1


Lesson Objective: NCSCOS 1.01 –
Write the equivalent forms of algebraic
expressions to solve problems
Students will know how to apply the
laws of exponents when multiplying
monomials.








Example 1Simplify: x2 * x3
Remember: x2 = x * x which can also be
written as xx
x2 = x * x and x3 = x * x * x
Therefore x2 * x3 = (x*x)*(x*x*x) = xx * xxx
= xxxxx
There are 5 x’s in the answer
Therefore x2 * x3 = x5
Rule: When multiplying monomials you must
add the exponents together. Xm * xn = xm+n
1.
33 * 34
2.
x3 * x4
3.
x5(x3)
4.
x7(x-2)
1.
33 * 34
37
2.
x3 * x4
x7
3.
x5(x3)
x8
4.
x7(x-2)
x5






Example 2Simplify (2x3)(3x4)
Multiply the numbers together first: 2 * 3 = 6
Multiply the variables together second: x3 * x4
= x7
Put the numbers and letters back together for
your answer: 6x7
Rule: When multiplying monomials you
multiply the numbers and letter separately
1.
3x3 * 4x2
2.
5x4(2x3)
3.
-2x2(4x)
4.
-7x(-3x3)
1.
3x3 * 4x2
12x5
2.
5x4(2x3)
10x7
3.
-2x2(4x)
-8x3
4.
-7x(-3x3)
21x4





Example 3Simplify (-2x2y3)(3x5y2)
Multiply the numbers together first:
–2 * 3 = -6
Multiply the x’s separately: x2 * x5 = x7
Multiply the y’s separately: y3 * y2 = y5
1.
3x3y2 * 4x2y2 12x5y4
2.
5x4y3(2x3y4)
10x7y7
3.
-2x2y2(4xy)
-8x3y3
4.
-7xy(-3x3y3)
21x4y4






Example 4
Simplify (x3)2
Remember, (x3)2 = (x3) * (x3) = xxx * xxx
Therefore (x3)2 = x6
Rule: When a monomial with an exponent is
then raised to an exponent you multiply the
exponents together. (Xm)n = xm*n
You can always write out x3 twice and add the
exponents
1.
(x2)3
2.
(x4)4
3.
(x3)7
1.
(x2)3
x6
2.
(x4)4
x16
3.
(x3)7
x21








Example 5
Simplify: 2x2(3x3)2
Remember order of operations, exponents come
before multiplication!
Also, any number squared means to multiply it by
itself
Therefore: 2x2(3x3)(3x3)
Multiply the numbers: 2 * 3 * 3 = 18
Multiply the variables: x2 * x3 * x3 = x8
Put the numbers and letters back together: 18x8
1.
2x2(3x3)2
2.
(4x3)2(2x5)
3.
(3x4)3(2x3)2
1.
2x2(3x3)2
2.
(4x3)2(2x5)
3.
(3x4)3(2x3)2 108x18
18x8
32x11
1.
2.
3.
4.
5.
x2 * x3
3x(2x3)
-2x3(4x4)
(x4)3
2x3(3x4)2
5
x
*
3x(2x3) 6x4
-2x3(4x4) -8x7
12
4
3
x
(x )
2x3(3x4)2 18x11
1. x2
2.
3.
4.
5.
x3