How do you multiply $(-2z^2 + 6z - 1)(- 4z^2)$ ?

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Answer 1 · 2015-04-10T09:50:29

We use the Distributive Property of Multiplication to solve this.

In general, $color(blue)((a+-b)*c = (a*b) +- (a*c)$

$(-2z^2 + 6z - 1)(- 4z^2)$

$= (-2z^2)*(-4z^2) + 6z(-4z^2) - (-4z^2)$

$= (-2*-4)(z^2*z^2)+ (6*(-4))(z*z^2) + 4z^2$

In general, $color(blue)( a^m*a^n = a^(m+n)$

$= (8)(z^(2+2))+ 6(-4)(z^(1+2)) + 4z^2$

$= 8z^4 + (-24)(z^3) + 4z^2$

$color(green)(= 8z^4 - 24z^3 + 4z^2$

How do you multiply (-2z^2 + 6z - 1)(- 4z^2)(-2z^2 + 6z - 1)(- 4z^2)?