Question: Please help me with this last step only. Thank you. Consider the following polynomial. 8 d 3 + 1 Identify the expressions that should be
Please help me with this last step only. Thank you.
Consider the following polynomial.
8d3+ 1
Identify the expressions that should be used foraandbin order to rewrite the expression as the sum of two cubes in the form
(a3+b3).
Step 1 of 2
Write the first term of the given expression as a perfect cube.
The first term in the given expression is
8d3.
The number8is a perfect cube, which can be written in exponential form.
8
=
222
=
3
2
Substitute the exponential form found above into the given expression. Then, use the power of product rule for exponents to rewrite the first term in the form
a3.
8d3+ 1
= (2)3d3+ 1
Step 2 of 2
Write the second term of the given expression as a perfect cube. Then, determine the needed expressions foraandb.
The second term in the given expression is 1. Remember that 1 raised to any powernequals 1, or
1n= 1.
Therefore, we can rewrite 1 as a perfect cube.
(2d)3+ 1 = (2d)3+13
The expression is now in the form
(a3+b3).
Therefore, what are the expressions that should be used foraandbin order to rewrite the expression as the sum of two cubes in the form
(a3+b3)?
Please help me with this last step. Thank you.
(Enter your answers as a comma-separated list.)
_______________________
Thank you.
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
