How do you simplify $(x + 1) (x^{2} + x + 1)$ $(x + 1)(x^2 + x + 1)$ ?

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How do you simplify $(x + 1) (x^{2} + x + 1)$ $(x + 1)(x^2 + x + 1)$ ?

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Answer 1 · 2017-03-12T18:12:25

See the entire simplification process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$(x + 1) (x^{2} + x + 1)$ $(color(red)(x) + color(red)(1))(color(blue)(x^2) + color(blue)(x) + color(blue)(1))$ becomes:

$(x \times x^{2}) + (x \times x) + (x \times 1) + (1 \times x^{2}) + (1 \times x) + (1 \times 1)$ $(color(red)(x) xx color(blue)(x^2)) + (color(red)(x) xx color(blue)(x)) + (color(red)(x) xx color(blue)(1)) + (color(red)(1) xx color(blue)(x^2)) + (color(red)(1) xx color(blue)(x)) + (color(red)(1) xx color(blue)(1))$

$x^{3} + x^{2} + x + x^{2} + x + 1$ $x^3 + x^2 + x + x^2 + x + 1$

We can now group and combine like terms:

$x^{3} + x^{2} + x^{2} + x + x + 1$ $x^3 + x^2 + x^2 + x + x + 1$

$x^{3} + 1 x^{2} + 1 x^{2} + 1 x + 1 x + 1$ $x^3 + 1x^2 + 1x^2 + 1x + 1x + 1$

$x^{3} + (1 + 1) x^{2} + (1 + 1) x + 1$ $x^3 + (1 + 1)x^2 + (1 + 1)x + 1$

$x^{3} + 2 x^{2} + 2 x + 1$ $x^3 + 2x^2 + 2x + 1$

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How do you simplify $(x + 1) (x^{2} + x + 1)$ $(x + 1)(x^2 + x + 1)$ ?

1 Answer

Explanation:

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How do you simplify $(x + 1) (x^{2} + x + 1)$ $(x + 1)(x^2 + x + 1)$ ?