Math  /  Algebra

QuestionMultiply. (r+t)(r2rt+t2)(r+t)(r2rt+t2)=\begin{array}{l} (r+t)\left(r^{2}-r t+t^{2}\right) \\ (r+t)\left(r^{2}-r t+t^{2}\right)= \end{array} \square (Simplify your answer.)

Studdy Solution

STEP 1

1. We need to multiply two binomials and simplify the resulting expression.
2. The distributive property will be used to expand the expression.

STEP 2

1. Apply the distributive property to multiply the binomials.
2. Simplify the resulting expression by combining like terms.

STEP 3

Apply the distributive property to multiply (r+t)(r+t) by each term in the polynomial (r2rt+t2)(r^2 - rt + t^2).
(r+t)(r2rt+t2)=r(r2rt+t2)+t(r2rt+t2)(r+t)(r^2 - rt + t^2) = r(r^2 - rt + t^2) + t(r^2 - rt + t^2)

STEP 4

Distribute rr across the terms in the polynomial:
r(r2rt+t2)=r3r2t+rt2r(r^2 - rt + t^2) = r^3 - r^2t + rt^2

STEP 5

Distribute tt across the terms in the polynomial:
t(r2rt+t2)=tr2t2r+t3t(r^2 - rt + t^2) = tr^2 - t^2r + t^3

STEP 6

Combine the results from the previous steps:
r3r2t+rt2+tr2t2r+t3r^3 - r^2t + rt^2 + tr^2 - t^2r + t^3

STEP 7

Combine like terms:
- Combine r2t-r^2t and tr2tr^2 to get 00. - Combine rt2rt^2 and t2r-t^2r to get 00.
The simplified expression is:
r3+t3r^3 + t^3
The simplified answer is:
r3+t3\boxed{r^3 + t^3}

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