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

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

2 Answers

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Answer 1 · 2018-03-31T05:06:40

$x^{4} + 4 x^{3} + 6 x^{2} + 8 x - 5$ $x^4+4x^3+6x^2+8x-5$

Explanation:

Just use a modified version of foil or a table

$x^{2} (x^{2} + 2 x + 5) = x^{4} + 2 x^{3} + 5 x^{2}$ $x^2(x^2+2x+5)=x^4+2x^3+5x^2$

$2 x (x^{2} + 2 x + 5) = 2 x^{3} + 2 x^{2} + 10 x$ $2x(x^2+2x+5)=2x^3+2x^2+10x$

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

Just add them all up

$x^{4} + 2 x^{3} + 5 x^{2} + 2 x^{3} + 2 x^{2} + 10 x - x^{2} - 2 x - 5$ $x^4+2x^3+5x^2+2x^3+2x^2+10x-x^2-2x-5$

$x^{4} + 2 x^{3} + 2 x^{3} + 5 x^{2} + 2 x^{2} - x^{2} + 10 x - 2 x - 5$ $x^4+color(red)(2x^3+2x^3)+color(blue)(5x^2+2x^2-x^2)+color(pink)(10x-2x)-5$

$x^{4} + 4 x^{3} + 6 x^{2} + 8 x - 5$ $x^4+color(red)(4x^3)+color(blue)(6x^2)+color(pink)(8x)-5$

Answer 2 · 2018-03-31T05:21:59

$x^{4} + 4 x^{3} + 8 x^{2} + 8 x - 5$ $x^4+4x^3+8x^2+8x-5$

Explanation:

Given-

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

$(x^{2} \times x^{2}) + (2 x \times x^{2}) - (1 \times x^{2}) + (x^{2} \times 2 x) + (2 x \times 2 x) - (1 \times 2 x) + (x^{2} \times 5) + (2 x \times 5) - (1 \times 5)$ $(x^2 xx x^2)+(2x xx x^2)-(1 xxx^2)+(x^2 xx 2x)+(2x xx 2x)-(1 xx 2x)+(x^2 xx5)+(2x xx5)-(1xx5)$

$x^{4} + 2 x^{3} - x^{2} + 2 x^{3} + 4 x^{2} - 2 x + 5 x^{2} + 10 x - 5$ $x^4+2x^3-x^2+2x^3+4x^2-2x+5x^2+10x-5$

$x^{4} + 2 x^{3} + 2 x^{3} - x^{2} + 4 x^{2} + 5 x^{2} - 2 x + 10 x - 5$ $x^4+2x^3+2x^3-x^2+4x^2+5x^2-2x+10x-5$

$x^{4} + 4 x^{3} + 8 x^{2} + 8 x - 5$ $x^4+4x^3+8x^2+8x-5$

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

2 Answers

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How do you multiply polynomials (x^2 + 2x - 1)(x^2 + 2x + 5)(x2+2x−1)(x2+2x+5)(x^2 + 2x - 1)(x^2 + 2x + 5)?

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