Question

What is the area of a square with sides of length 2x + 7? Write your answer in polynomial form.

Answer 1

Remember - the area of a square is one side whole squared.

Answer 2

\[ Area = (2 x + 7)^2\]

Answer 3

so im not really sure what am i suppose to do?

Answer 4

\[ (2x + 7)^2 \implies (2x + 7)(2x + 7)\]

Answer 5

ooh, am i suppose to multiply?

Answer 6

Ya

Answer 7

so is that suppose 2 become 4x+49?

Answer 8

Nope.

Answer 9

hmm so what do i do?

Answer 10

\[(2x + 7)(2x + 7) \implies 2x(2x + 7) + 7(2x + 7) \]Use the distributive property now.

Answer 11

so you get 4x+14+14x+49 and then dont i do 4x+14x=18x , and then 49+14=63 so get 18x+63?

Answer 12

4x^2*

Answer 13

ooh, so is it really 18x^2+63?

Answer 14

Nope.\[4x^2 + 14x + 14x + 49 \]What you can do is add 14x + 14x.

Answer 15

to get 28x

Answer 16

Yes.\[ 4x^2 + 28x + 49\]

Answer 17

No wait that was correct.

Answer 18

Yeah. It's 4x^2 + 28x + 49

Answer 19

so the right answer is 4x^2+28x+49?

Answer 20

Yep.

Answer 21

okay is that all we do to it?

Answer 22

Yes - that's it.

Answer 23

okay thanks alot again :)

Answer 24

You're welcome!

Answer 25

\[\Large{\color{green}{{Area \space \space of \space a \space SQUARE = side \times side}}}\]\[\Large{area=(2x+7)(2x+7)=(2x+7)^2}\]Now use the formula\[\Large{(a+b)^2=a^2+2ab+b^2\Huge{\color{red}{\checkmark}}}\]