Question

three questions please. Can you explain? Medal
What is the factored form of these expressions?
1. d^2 + 18d + 81
2. r^2 + 20r +100
3. t^2 - 25

Answer 1

I assume simplify?
\[d^2 + 18d + 81\]\[(d+9)^2\]
\[r^2 + 20r +100\]\[(r+10)^2\]
\[t^2-25\]\[t^2-5^2\]\[(t+5)(t-5)\]The first two use the law: \[(a+b)^2=(a^2+2ab+b^2)\]The second law uses the fact\[x^2+y^2=(x+y)(x-y)\]

Answer 2

So I got to use those two laws to solve questions like these?

Answer 3

Please explain, I want to make sure i get this for starr

Answer 4

@Romantic_Ch3micals , yes :) These two laws allow you to easliy factor those kind of equations.

Ok, imaging this:
\[x^2-36\]
We can turn 36 to have a power\[x^2-6^2\]If we look at the law \(x^2-y^2\), we see that it is similar to the equation we have. \(x^2-y^2=(x-y)(x+y)\). Lets do that for our one.
\[x^2-36\]\[x^2-9^2\]\[(x-9)(x+9)\]And thats it :) Expand if you wish, and you will get the same answer