Transcript document
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