How do you simplify $(x^{2} + 3 x + 10) (4 x^{2} - 2 x - 7)$ $(x^2 + 3x + 10)(4x^2 - 2x - 7)$ ?

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How do you simplify $(x^{2} + 3 x + 10) (4 x^{2} - 2 x - 7)$ $(x^2 + 3x + 10)(4x^2 - 2x - 7)$ ?

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Answer 1 · 2018-07-17T06:30:46

$= 4 x^{4} + 10 x^{3} + 27 x^{2} - 41 x - 70$ $=4x^4+10x^3+27x^2-41x-70$

Explanation:

Each term in the first bracket has to be multiplied by each term in the second bracket.

$(x^{2} + 3 x + 10) (4 x^{2} - 2 x - 7)$ $(color(red)(x^2) +color(blue)(3x)+color(green)(10))(4x^2-2x-7)$

$= x^{2} (4 x^{2} - 2 x - 7) + 3 x (4 x^{2} - 2 x - 7) + 10 (4 x^{2} - 2 x - 7)$ $=color(red)(x^2)(4x^2-2x-7) +color(blue)(3x)(4x^2-2x-7)+color(green)(10)(4x^2-2x-7)$

$= 4 x^{4} - 2 x^{3} - 7 x^{2} + 12 x^{3} - 6 x^{2} - 21 x + 40 x^{2} - 20 x - 70$ $=color(red)(4x^4-2x^3-7x^2) +color(blue)(12x^3-6x^2-21x)+color(green)(40x^2-20x-70)$

Now simplify by collecting the like terms,

$= (4 x^{4}) + (- 2 x^{3} + 12 x^{3}) + (- 7 x^{2} - 6 x^{2} + 40 x^{2}) + (- 21 x - 20 x) + (- 70)$ $=(4x^4)+(-2x^3+12x^3)+(-7x^2-6x^2+40x^2)+(-21x-20x)+(-70)$

$= 4 x^{4} + 10 x^{3} + 27 x^{2} - 41 x - 70$ $=4x^4+10x^3+27x^2-41x-70$

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How do you simplify $(x^{2} + 3 x + 10) (4 x^{2} - 2 x - 7)$ $(x^2 + 3x + 10)(4x^2 - 2x - 7)$ ?

1 Answer

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How do you simplify (x^2 + 3x + 10)(4x^2 - 2x - 7)(x2+3x+10)(4x2−2x−7)(x^2 + 3x + 10)(4x^2 - 2x - 7)?

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Explanation:

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How do you simplify $(x^{2} + 3 x + 10) (4 x^{2} - 2 x - 7)$ $(x^2 + 3x + 10)(4x^2 - 2x - 7)$ ?