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How do you multiply $(2 b - 1) (b^{2} - 3 b + 4)$ $(2b-1)(b^2-3b+4)$ ?

1 Answer

Jun 26, 2018

$2 b^{3} - 4 b^{2} + 11 b - 4$ $color(red)(2b^3-4b^2+11b-4)$

Explanation:

$(2 b - 1) (b^{2} - 3 b + 4)$ $color(magenta)(""(2b-1))(b^2-3b+4)$

using the distributive property:
$XXX = 2 b (b^{2} - 3 b + 4) xxxx - 1 (b^{2} - 3 b + 4)$ $color(white)("XXX")=color(magenta)(2b)(b^2-3b+4)color(white)("xxxx")color(magenta)(-1)(b^2-3b+4)$

$XXX = 2 b^{3} - 3 b^{2} + 8 b \times \times - b^{2} + 3 b - 4$ $color(white)("XXX")=2b^3-3b^2+8bcolor(white)("xxxx)-b^2+3b-4$

combining like terms:
$XXX = 2 b^{3} - 4 b^{2} + 11 b - 4$ $color(white)("XXX")=2b^3-4b^2+11b-4$

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