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How do you simplify $- a \cdot - a$ $-a * -a$ ?

2 Answers

Mar 16, 2017

$(- a) \cdot (- a) = a^{2}$ $(-a) * (-a) = color(green)(a^2)$

Explanation:

$(- a) \cdot (- a) XXX$ $(-a) * (-a)color(white)("XXX")$ I've added the parentheses
$XXXXXXXXXXX$ $color(white)("XXXXXXXXXXX")$ since having multiple operators in a row can be confusing.

$XXX = (- 1) \cdot a \cdot (- 1) \cdot a$ $color(white)("XXX")=(-1) * a * (-1) * a$

$XXX = (- 1) \cdot (- 1) \cdot a \cdot a$ $color(white)("XXX")=(-1) * (-1) * a * a$

$XXX = + 1 \cdot a^{2}$ $color(white)("XXX")=+1 * a^2$

$XXX = a^{2}$ $color(white)("XXX")=a^2$

Mar 16, 2017

See the entire simplification process below:

Explanation:

Use these two rules of exponents to simplify this expression:

$a = a^{1}$ $a = a^color(red)(1)$ and $x^{a} \times x^{b} = x^{a + b}$ $x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))$

$- a \cdot - a = - a^{1} \cdot - a^{1} = {(- a)}^{1 + 1} = {(- a)}^{2}$ $-a * -a = -a^color(red)(1) * -a^color(blue)(1) = (-a)^(color(red)(1) + color(blue)(1)) = (-a)^2$

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