Suppose you have a square whose length and width are x units. If you increase the length by 3 units, what is the area of the new figure?
You can
model this problem by using algebra tiles. The figures show how to make a
rectangle whose length is x + 3 units and whose width is x units.
The area of
any rectangle is the product of its length and its width. The area can also be found by adding the areas of the tiles.
Formula Algebra Tiles
A = lw A = x2 + x + x + x
= (x + 3) x or x(x
+ 3) = x2
+ 3x
= x2 + 3x
Since the
areas are equal, x(x + 3) = x2 + 3x.
Another expression for the same area is x2 + 3x square
units.
The example
above shows how the Distributive Property can be used to multiply a polynomial
by a monomial.
Find each
product.
1.
y(y + 5)
Alternative Solutions:
y(y + 5) = y(y) +
y(5)
= y2 +5y
2.
b(2b2 + 3)
Alternative Solutions:
b(2b2 + 3) = b(2b2)
+ b(3)
= 2b3
+ 3b
= y2 +5y
3.
–2n(7 – 5n2)
Alternative Solutions:
–2n(7 – 5n2)
= –2n(7) + (–2n) (–5n2)
= –14n + 10n3
4.
3x3(2x2 – 5x + 8)
Alternative Solutions:
3x3(2x2
– 5x + 8) = 3x3(2x2)
+ 3x3(–5x) + 3x3(8)
= 6x5 – 15x4
+ 24x3
Many
equations contain polynomials that must be multiplied.
Example
Solve
each equation.
5.
11(y – 3) + 5 = 2(y + 22)
Alternative Solutions:
6.
w(w + 12) = w(w + 14) + 12
Alternative Solutions:
You can
apply multiplication of a polynomial by a monomial to problems involving area.
Geometry
Link
7.
Find
the area of the shaded region in simplest form.
Alternative Solutions:
Subtract the area of the
smaller rectangle from the area of the larger rectangle.
Sumber
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