Katie has a square herb garden in which she grows parsley.
The measure of each
side is x feet. She wants to increase the length by 2 feet and the width
by 1 foot
so she can grow sage, rosemary, and thyme. A plan for the garden is shown at
the right. Find two different expressions for the area of the new garden.
.PNG)
One way to find the area of the garden is to use the formula
for area. Find the product of the length and width of the new garden.
Formula
A =
lw
= (x + 2)(x
+ 1)
You can also find the area by adding the areas of the smaller
regions.
Sum of Regions
Since the areas are equal, both expressions are equal.
Therefore,
(x + 2)(x + 1) = x2 + 3x +
2.
The multiplication expression can also be shown in the model
below. Notice that the Distributive Property is used twice.
So, (x + 2)(x + 1) = x2 + 1x
+ 2x + 2 or x2 + 3x + 2.
You can also use the Distributive Property to multiply
binomials.
Find each product.
1.
(x + 3)(x – 4)
Alternative Solutions:
2.
(2y – 1)(y – 3)
Alternative Solutions:
Two
binomials can always be multiplied using the Distributive Property. However,
the following shortcut can also be used. It is called the FOIL method.
Example
Find each product.
3.
(y + 4)(y + 6)
Alternative Solutions:
4.
(2x – 3)(2x + 2)
Alternative Solutions:
5.
(3a – b)(2a + 4b)
Alternative Solutions:
Sometimes it is not possible to simplify the product of two
binomials.
Example
6. Find the product of x2
– 4 and x + 3.
Alternative Solutions:
You can use the FOIL method to solve problems involving
volume.
Geometry
Link
7. The volume V of a rectangular prism
is equal to the area of the base B times the height h. Express the
volume of the prism as a polynomial. Use V = Bh.
Alternative Solutions:
First,
find the area of the base. The base is a rectangle.
The volume
of the prism is x3 + 5x2 – 6x cubic
units.
Sumber
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