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

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Answer 1 · 2018-07-17T06:30:46

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

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

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

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

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

Now simplify by collecting the like terms,

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

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

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