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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(2x+4)
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(6x+2)
•3(-x-1)
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(2x+4) we can
show the length of the rectangle as 2x+4
and the width as 3.
 You
then fill in the area under the length
and width of the ractangle with algebra
tiles to determine the area, or product.
Try these using the area model
 4(2x+3)
 2(3x+5)
 3x(2x+6)
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.
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.
Examples
3(x + 2)
3x(x + 1)
4(2x + 3)
= 3(x) + 3(2)
= 3x(x) + 3x(1) = 4(2x) + 4(3)
= 3x + 6
= 3x2 + 3x
= 8x + 12
Remember that each term
is being multiplied by the
monomial outside the
brackets
Expanding
 Using
the Distributive Law in algebra is
called EXPANDING.
 Example:
8x(x – 3)
8x(x) – 8x(3)
8x2 – 24x
Expand
t( t – x – 2)
3(g2 – 3g + 1)
= t(t) – t(x) – t(2)
= 3(g2) – 3(3g) + 3(1)
= t2 – tx – 2t
= 3g2 – 9g + 3
Remember that when you
expand, each term is being
multiplied by the monomial
outside the brackets
5(a + 3)
-6(x2 - 4)
x2(2x + 8)
2(a2 +3a - 5)
3x(-2x2 - 5x + 6)
Class work
 Lesson
25 worksheet