Caleb Snyder

2022-01-29

How do you write in standard form y=4(x+5)-2(x+1)(x+1)?

baltimi

Expert

Explanation:
Since this expression has many parts, I will color-code it and tackle it one by one.
4(x+5)-2(x+1)(x+1)
For the expression in purple, all we need to do is distribute the 4 to both terms in the parenthesis. Doing this, we now have
4x+20-2(x+1)(x+1)
What I have in blue, we can multiply with the mnemonic FOIL, which stands for Firsts, Outsides, Insides, Lasts. This is the order we multiply the terms in.
Foiling (x+1)(x+1):
First terms: $x\cdot x={x}^{2}$
Outside terms: x*1=x
Inside terms: 1*x=x
Last terms: 1*1=1
This simplifies to ${x}^{2}+2x+1$. We now have
$4x+20-2\left({x}^{2}+2x+1\right)$
Distributing the -2 to the blue terms gives us
$4x+20-2{x}^{2}-4x-2$
Combining like terms gives us
$-2{x}^{2}+18$
We see that our polynomial is in standard form, $a{x}^{2}+bx+c$. Notice that the x terms cancel out, so we don't have a bx term.

Do you have a similar question?