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.

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