How do you multiply $(2 x - 5) (6 x^{2} - 6 x - 11)$ $(2x - 5) ( 6x ^ { 2} - 6x - 11)$ ?

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Answer 1 · 2018-05-01T16:03:07

$12 x^{3} - 42 x^{2} + 8 x + 55$ $12x^3-42x^2+8x+55$

Simply multiply each term in each bracket, but not terms in the same bracket.

$(2 x - 5) (6 x^{2} - 6 x - 11)$ $(color(red)(2x)color(blue)(-5))(color(green)(6x^2)color(red)(-6x)color(blue)(-11))$

$2 x \times 6 x^{2} = 12 x^{3}$ $color(red)(2x) xx color(green)(6x^2)=color(orange)(12x^3)$

$2 x \times - 6 x = - 12 x^{2}$ $color(red)(2x) xx color(red)(-6x)=color(green)(-12x^2)$

$2 x \times - 11 = - 22 x$ $color(red)(2x) xx color(blue)(-11)=color(red)(-22x)$

$- 5 \times 6 x^{2} = - 30 x^{3}$ $color(blue)(-5) xx color(green)(6x^2)=color(green)(-30x^3)$

$- 5 \times - 6 x = 30 x$ $color(blue)(-5) xx color(red)(-6x)=color(red)(30x)$

$- 5 \times - 11 = 55$ $color(blue)(-5) xx color(blue)(-11)=color(blue)(55)$

Collect like terms:

$12 x^{3} - 12 x^{2} - 30 x^{2} - 22 x + 30 x + 55$ $color(orange)(12x^3)color(green)(-12x^2-30x^2)color(red)(-22x+30x)color(blue)(+55)$

$\Rightarrow 12 x^{3} - 42 x^{2} + 8 x + 55$ $rArr color(orange)(12x^3)color(green)(-42x^2)color(red)(+8x)color(blue)(+55)$

$\Rightarrow 12 x^{3} - 42 x^{2} + 8 x + 55$ $rArr 12x^3-42x^2+8x+55$

How do you multiply (2x−5)(6x2−6x−11)(2x - 5) ( 6x ^ { 2} - 6x - 11)?