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

Caleb Snyder

Caleb Snyder

Answered

2022-01-29

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

Answer & Explanation

baltimi

baltimi

Expert

2022-01-30Added 7 answers

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: xx=x2
Outside terms: x*1=x
Inside terms: 1*x=x
Last terms: 1*1=1
This simplifies to x2+2x+1. We now have
4x+202(x2+2x+1)
Distributing the -2 to the blue terms gives us
4x+202x24x2
Combining like terms gives us
2x2+18
We see that our polynomial is in standard form, ax2+bx+c. Notice that the x terms cancel out, so we don't have a bx term.

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