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

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Answer 1 · 2015-04-10T09:50:29

We use the Distributive Property of Multiplication to solve this.

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

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

$= (- 2 z^{2}) \cdot (- 4 z^{2}) + 6 z (- 4 z^{2}) - (- 4 z^{2})$ $= (-2z^2)*(-4z^2) + 6z(-4z^2) - (-4z^2)$

$= (- 2 \cdot - 4) (z^{2} \cdot z^{2}) + (6 \cdot (- 4)) (z \cdot z^{2}) + 4 z^{2}$ $= (-2*-4)(z^2*z^2)+ (6*(-4))(z*z^2) + 4z^2$

In general, $a^{m} \cdot a^{n} = a^{m + n}$ $color(blue)( a^m*a^n = a^(m+n)$

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

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

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

How do you multiply (−2z2+6z−1)(−4z2)(-2z^2 + 6z - 1)(- 4z^2)?