How do you find the product of #(a+5)(a-6)#?

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Answer 1 · 2018-04-28T20:19:32

#a^2 - a - 30#

To solve this, we expand/distribute using FOIL:
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As you can see in this image, the first thing we do is multiply the #color(steelblue)"firsts"#:
#a * a = a^2#

Then the #color(purple)"outers"#:
#a * -6 = -6a#

Then the #color(peru)"inners"#:
#5 * a = 5a#

and finally the #color(olivedrab)"lasts"#:
#5 * -6 = -30#

Now combine them all together:
#a^2 - 6a + 5a - 30#

We can still simplify the like terms. Let's color-code them:
#a^2 quadcolor(red)(-quad6a quad+quad 5a) quad - quad30#

Combine like terms and get the final answer:
#a^2 - a - 30#

Hope this helps!

Answer 2 · 2018-06-30T22:27:44

#a^2-a -30#

#color(blue)((a+5))color(green)( (a-6) )#

Multiply everything in the right brackets (green) by everything in the left brackets (blue).

#color(green)(color(blue)(a)(a-6) color(white)("ddd")color(blue)(+5)(a-6) )#

Notice that the + sign followed the 5

#a^2-6acolor(white)("dd")+5a-30#

but #-6a+5a# is the same as #-a# giving.

#a^2-a -30#