Product of Three Binomials
Algebra Help: Section 2.18
Apply the principles established in the last few sections, to save a lot of labor. Use the rules to find the product of three or more binomials.
1. What is the value of
(x + 3)
(x + 3)
(x + 3)
when expanded?
x2 + 6x + 9
x + 3
___________________
x3 + 6x2 + 9x
3x2 + 18x + 27
___________________
x3 + 9x2 + 27x + 27
ANALYSIS -
We start with knowledge gained from studying
a + b times
a + b, previously.
We know
(x + 3) times
(x + 3)
equals x2 + 6x + 9.
Next we multiply x2 + 6x + 9
by x + 3, which equals
x3 + 6x2 + 9x with
3x2 + 18x + 27
Last sum the two products; x3 + 6x2 + 9,
with 3x2 + 18x + 27 equals
x3 + 9x2 + 27x + 27.
2. Expand
(a + b)
(a - b)
(a - c)
OPERATION:
(a + b)(a - b) = a2 - b2
a2 - b2
a - c
_____________________
a3 - ab2
- a2c + b2c
_____________________
a3 - ab2 - a2c + b2c
ANALYSIS -
Expand (a + b)(a - b)
by the rule described in section
Multiply Sum & Difference of Two Quantities.
Then multiply the result by (a - c).
3. Expand
(x - c)
(x - d)
(x + c)
(x + d)
OPERATION:
x2 - c2
x2 - d2
______________________
x4 - x2c2
- d2x2 + c2d2
______________________
x4 - x2c2 - d2x2 + c2d2
ANALYSIS - Again, use the rule described in section Multiply Sum & Difference of Two Quantities.
Rearrange factors
(x + c)
(x - c) equals
x2 - c2.
Rearrange factors
(x + d)
(x - d) equals
x2 - d2.
Multiply the two factors together:
x2 - c2 times
x2 - d2
NOTE - In obtaining the continued product of several factors, the student should use judgment in selecting and combining the factors. Ideally apply rules mentally, to write as little as possible.
Page 51-52
Page 51-52
Help with Algebra Homework
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New Elementary Algebra
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By Horation N Robinison, LL. D. Ivison, Blakeman & Company, Publishers, New York and Chicago.
