Multiplying Polynomials
How do we find the area of a
square?
A s
2
The correct formula is written above.
Use it to find the area of the square below.
X
X
As we have already said, to find the area, we
square the length of a side.
X
X
Ax
2
What happens to the area if we
add 3 units to the length and 1 unit
to the width?
1
X
X
---------3--------
This definitely increases the area.
How can we find the area of the
new shape?
One way would be to add the areas
of the individual rectangles that we
have formed.
1
X
3
x2  x  3x  3
X
X2
3x
X
---------3--------
x2  4x  3
Another way of doing this would
be using the formula for the
area of a rectangle?
A=lw
1
A=(x+3)(x+1)
X
X
---------3--------
How do we get from (x+3)(x+1) to x2  4x  3 ?
We have already seen that 2(x+1) = 2x+2
We were able to do this multiplication by using the
distributive property. We can also use the
distributive property when we are multiplying
polynomials by polynomials.
We need to remember to distribute each
term in the first set of parentheses through
the second set of parentheses.
Example:
(X+3)(x+1)=(x)(x)+(x)(1)+(3)(x)+(3)((1)
x  x  3x  3
2
x  4x  3
2
Let’s work a few of these.
1.) (x+2) (x+8)
2.) (x+5) (x-7)
3.) (2x+4) (2x-3)
Check your answers.
1.) (x+2) (x+8) =
X2+10x+16
2.) (x+5) (x-7) =
X2-2x-35
3.) (2x+4) (2x-3) = 4x2+2x-12
By learning to use the distributive property, you
will be able to multiply any type of polynomials.
Example: (x+1)(x2+2x+3)
(x+1)(x2+2x+3) = X3+2x2+3x+x2+2x+3
 x3  3x2  5x  3