The cube
of a binomial is simply a binomial multiplied to itself three times. By expounding,
a cube is a geometrical figure with three dimensions which is used to
refer thrice of a variable in algebraic expressions while a binomial consists
of two terms expressing either the sum or difference. See the other links below for
reference
https://brainly.ph/question/66188
https://brainly.ph/question/577414
Knowing how
to solve the cube of a binomial step by step takes practice with lots of exercises.
The two examples below will show the two-step solution both for addition and
subtraction.
Example 1
(p+a)^3
= (p+a) (p+a) (p+a)
Extract the binomial cube to better understand the
process.
Step1
Multiply the first two binomials
p+a
* p+a
_______
pa+a^2
p^2+pa
___________
p^2+2pa+a^2
Step 2
Multiply the answer from Step 1 to the third
binomial
p^2+2pa+a^2
* p+a
___________
p^2a +2pa^2
+a^3
p^3+ 2p^2a + pa^2 (add
the like terms to simplify)
____________
p^3+ 3p^2a + 3pa^2 +a^3
Looking at the answer, the cube
of a binomial is the cube of the 1st term (p^3) plus thrice
of the square of the 1st term times the 2nd term (3p^2a)
plus thrice of the 1st term multiplied to the square of the 2nd
term (3pa^2) plus the cube of the 2nd term (a^3). This is the standard pattern for a binomial cube with addition (plus sign). Another example is
found in https://brainly.ph/question/683550
The next example will show the contrast with subtraction.
Example 2
(p-a)^3
= (p-a) (p-a) (p-a)
Step1
Multiply the first two binomials
p-a
* p-a
______
pa-a^2
p^2-pa
________
p^2-2pa+a^2
Step 2
Multiply the answer from Step 1 to the third
binomial
p^2-2pa+a^2
* p-a
________
-p^2a+2pa^2 -a^3
p^3- 2p^2a + pa^2
______________
p^3-3p^2a+3pa^2-a^3
The cube
of a binomial expressed in subtraction has the same pattern with the first example except that the
2nd and 4th values in the second example are both negative. Another
example is found in https://brainly.ph/question/933003
