How do you simplify $(x - 1) (x^{2} + 5 x - 2)$ $(x -1)(x^2+ 5x-2)$ ?

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How do you simplify $(x - 1) (x^{2} + 5 x - 2)$ $(x -1)(x^2+ 5x-2)$ ?

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Answer 1 · 2016-10-24T09:59:13

$x^{3} + 4 x^{2} - 7 x + 2$ $x^3+4x^2-7x+2$

Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket.
This can be achieved as follows.

$(x - 1) (x^{2} + 5 x - 2)$ $(color(red)(x-1))(color(blue)(x^2+5x-2))$

$= x (x^{2} + 5 x - 2) - 1 (x^{2} + 5 x - 2)$ $=color(red)(x)(color(blue)(x^2+5x-2))color(red)(-1)(color(blue)(x^2+5x-2))$

distribute the brackets.

$= x^{3} + 5 x^{2} - 2 x - x^{2} - 5 x + 2$ $=x^3+5x^2-2x-x^2-5x+2$

collect like terms.

$x^{3} + (5 x^{2} - x^{2}) + (- 2 x - 5 x) + 2$ $x^3+(5x^2-x^2)+(-2x-5x)+2$

$= x^{3} + 4 x^{2} - 7 x + 2$ $=x^3+4x^2-7x+2$

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How do you simplify $(x - 1) (x^{2} + 5 x - 2)$ $(x -1)(x^2+ 5x-2)$ ?

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How do you simplify $(x - 1) (x^{2} + 5 x - 2)$ $(x -1)(x^2+ 5x-2)$ ?