How do you simplify $5 (x - 4) (x + 1 + i) (x - 1 - i)$ $5(x - 4)(x + 1 + i)(x - 1 - i)$ ?

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How do you simplify $5 (x - 4) (x + 1 + i) (x - 1 - i)$ $5(x - 4)(x + 1 + i)(x - 1 - i)$ ?

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Answer 1 · 2018-05-22T13:05:19

$5 x^{3} - 20 x^{2} - 10 x i + 40 i$ $5x^3-20x^2-10x i+40i$

Explanation:

$expand the factors in pairs and multiply the expansions$ $"expand the factors in pairs and multiply the expansions"$

$\Rightarrow 5 (x - 4) = 5 x - 20$ $rArr5(x-4)=5x-20$

$((x + 1) + i) ((x - 1) - i) \leftarrow expand using FOIL$ $((x+1)+i)((x-1)-i)larrcolor(blue)"expand using FOIL"$

$= (x + 1) (x - 1) - i (x + 1) + i (x - 1) - i^{2}$ $=(x+1)(x-1)-i(x+1)+i(x-1)-i^2$

$= x^{2} - 1 - x i - i + x i - i + 1 \to i^{2} = - 1$ $=x^2-1-x i-i+x i-i+1toi^2=-1$

$= x^{2} - 2 i$ $=x^2-2i$

$\Rightarrow (5 x - 20) (x^{2} - 2 i)$ $rArr(5x-20)(x^2-2i)$

$= 5 x^{3} - 10 x i - 20 x^{2} + 40 i$ $=5x^3-10x i-20x^2+40i$

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How do you simplify $5 (x - 4) (x + 1 + i) (x - 1 - i)$ $5(x - 4)(x + 1 + i)(x - 1 - i)$ ?

1 Answer

Explanation:

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How do you simplify 5(x−4)(x+1+i)(x−1−i)5(x - 4)(x + 1 + i)(x - 1 - i)?

1 Answer

Explanation:

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How do you simplify $5 (x - 4) (x + 1 + i) (x - 1 - i)$ $5(x - 4)(x + 1 + i)(x - 1 - i)$ ?