contestada

[tex] \frac{(a-3) * (\frac{a}{3} +1)}{\frac{1}{3}} [/tex]

[tex] \frac{a( \frac{a}{3} ) + a - 3(\frac{a}{3}) - 3 }{\frac{a}{3}} [/tex]

[tex] \frac{\frac{3a+a}{3} + a - 3 * \frac{a}{3} - 3}{\frac{1}{3}} [/tex]

[tex] \frac{\frac{4a}{3} + a - a - 3}{\frac{1}{3}} [/tex]

[tex] \frac{4a}{3} / \frac{1}{3} - 3 / \frac{1}{3} [/tex]

[tex] \frac{4a}{3} * 3 - 3 * 3 [/tex]

[tex] 4a - 9 [/tex]
Yet the answer I should get is [tex] a^{2}-9 [/tex]. What step am I doing wrong on this algebra problem?

Respuesta :

[tex] \bf \cfrac{(a-3)\left( \frac{a}{3}+1 \right)}{\frac{1}{3}}\implies 3\left[ (a-3)\left( \frac{a}{3}+1 \right) \right]
\\\\\\
3\left[\frac{a^2}{3}+a-a-3 \right]\implies 3\left[\frac{a^2}{3}-3 \right]\implies a^2-9 [/tex]

when you have polynomials multiplication, say (x+y) (a+b+c), you can always just multiply x(a+b+c) + y(a+b+c), namely each term by all others and sum them up, like above.