Multiplying a Polynomial

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Multiplying a Polynomial by a Monomial

Lesson 25
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Multiplying is Repeated addition

• You know that multiplying a number by 3 (example)
  is the same as adding 3 copies of that number.
  The same applies to polynomials. We can show
  that using algebra tiles
• Example 3(2x4)

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Try this in your groups

• use algebra tiles to work out these problems
• each person should draw and write each expression
• 4(3x-3)
• 2(6x2)
• 3(-x-1)

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We can also use the area model

• The area of a rectangle is the product of the
  length times width.
• Using the last example 3(2x4) we can show the
  length of the rectangle as 2x4 and the width as
  3.

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• You then fill in the area under the length and
  width of the ractangle with algebra tiles to
  determine the area, or product.

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Try these using the area model

• 4(2x3)
• 2(3x5)
• 3x(2x6)

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Distributive Law

• In mental math we have used what is called the
  distributive law to help us multiply big numbers.
• Example 3 x 27 3(20 7)
• 3(20) 3(7)
• 60 21
• 81

Multiply the number on the outside by all the
terms on the inside.
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Distributive Law

• We can apply the same concept to multiply
  polynomials by monomials.
• Just remember to multiply every term inside the
  brackets by the monomial outside the brackets.

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Examples

3(x 2) 3(x) 3(2) 3x 6
4(2x 3) 4(2x) 4(3) 8x 12
3x(x 1) 3x(x) 3x(1) 3x2 3x
Remember that each term is being multiplied by
the monomial outside the brackets
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Expanding

• Using the Distributive Law in algebra is called
  EXPANDING.
• Example 8x(x 3)

8x(x) 8x(3) 8x2 24x
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Expand
t( t x 2) t(t) t(x) t(2) t2 tx 2t
3(g2 3g 1) 3(g2) 3(3g) 3(1) 3g2 9g
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Remember that when you expand, each term is being
multiplied by the monomial outside the brackets
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TRY THESE!
5(a 3)
-6(x2 - 4)

x2(2x 8)
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TRY THESE!
2(a2 3a - 5)
3x(-2x2 - 5x 6)

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Class work

• Lesson 25 worksheet