Math  /  Algebra

QuestionFactor by grouping. x3+9x2+9x+81x^{3}+9 x^{2}+9 x+81

Studdy Solution

STEP 1

1. The expression x3+9x2+9x+81x^{3}+9x^{2}+9x+81 can be factored by grouping.
2. Grouping involves rearranging and factoring parts of the expression to simplify it.

STEP 2

1. Group the terms in pairs.
2. Factor out the greatest common factor from each group.
3. Identify and factor out the common binomial factor.

STEP 3

Group the terms in pairs:
(x3+9x2)+(9x+81) (x^{3} + 9x^{2}) + (9x + 81)

STEP 4

Factor out the greatest common factor from each group:
From the first group (x3+9x2)(x^{3} + 9x^{2}), factor out x2x^{2}:
x2(x+9) x^{2}(x + 9)
From the second group (9x+81)(9x + 81), factor out 99:
9(x+9) 9(x + 9)
Now the expression is:
x2(x+9)+9(x+9) x^{2}(x + 9) + 9(x + 9)

STEP 5

Identify and factor out the common binomial factor (x+9)(x + 9):
(x+9)(x2+9) (x + 9)(x^{2} + 9)
This is the factored form of the original expression.
The factored expression is:
(x+9)(x2+9) \boxed{(x + 9)(x^{2} + 9)}

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