Thread: Order of Operations confused

So i was working through my math book and i got to some questions about Order of Operations or BEDMAS (brackets, exponents, division, multiplication, adding, subtracting)

now im used to doing it but not with variables included i tried to figure it out but i just have no idea.

the questions are

2(x + 3)(x + 4) =

also when there is an exponent included

3(x + 3)^2 =


any help would be appreciated

Originally Posted by tomtomgreg

So i was working through my math book and i got to some questions about Order of Operations or BEDMAS (brackets, exponents, division, multiplication, adding, subtracting)

now im used to doing it but not with variables included i tried to figure it out but i just have no idea.

the questions are

2(x + 3)(x + 4) =

also when there is an exponent included

3(x + 3)^2 =


any help would be appreciated

(a+b)(c+d) = ac+ad+bc+bd nothing new here right?

2(x + 3)(x + 4) = ?

First you substitute whatever x is, then you work out the number inside the brackets(brackets first). Then you multiply them together(multiplication after).

3(x + 3)^2 = ?

First you substitute whatever x is into the equation, then you solve the brackets, then do to the power of 2, then multiply by 3.

Originally Posted by Educated

2(x + 3)(x + 4) = ?

First you substitute whatever x is, then you work out the number inside the brackets(brackets first). Then you multiply them together(multiplication after).

3(x + 3)^2 = ?

First you substitute whatever x is into the equation, then you solve the brackets, then do to the power of 2, then multiply by 3.

for example on the second question i have the answer key but i can't figure out how to run the operation.
The work book doesn't state what the variable is.

the answer to 3(x + 3)^2 = (according to my work book is) 3x^2 + 18x + 27

i don't even know how it got that...

That is called expanding the brackets.

You can use the FOIL method to expand it:

First - multiply the first value in the first bracket by the first value in the second bracket
Outer - multiply the first value in the first bracket by the last value in the second bracket
Inner - multiply the last value in the first bracket by the first value in the second bracket
Last - multiply the last value in the first bracket by the last value in the second bracket
Then multiply everything by whatever is outside of the brackets.

If you do not understand it, look up expanding brackets.

Originally Posted by tomtomgreg

for example on the second question i have the answer key but i can't figure out how to run the operation.
The work book doesn't state what the variable is.

the answer to 3(x + 3)^2 = (according to my work book is) 3x^2 + 18x + 27

i don't even know how it got that...

3(x+3)^2 = 3(x^2+6x+9) = 3x^2+18x+27

If you haven't been taught that (x+3)^2 = x^2+6x+9 then the question should not have been given to you in the first place.

so would i run it like

= 3(x + 3)^2
= 3(x + 3)(x + 3)
= 3 (x^x) (x^3) (3^x) (3^3)
= 3 (x^2) (3x) (3x) (9)
= 3 x^2 6x 9
= 3x^2 + 18x + 27

Originally Posted by undefined

3(x+3)^2 = 3(x^2+6x+9) = 3x^2+18x+27

If you haven't been taught that (x+3)^2 = x^2+6x+9 then the question should not have been given to you in the first place.

well in my work book i was working on polynomials and then these questions came up and i guess i didn't make the connection to using FOIL, thanks for the help though

Originally Posted by tomtomgreg

so would i run it like

= 3(x + 3)^2
= 3(x + 3)(x + 3)
= 3 (x^x) (x^3) (3^x) (3^3)
= 3 (x^2) (3x) (3x) (9)
= 3 x^2 6x 9
= 3x^2 + 18x + 27

This line

= 3 (x^x) (x^3) (3^x) (3^3)

should instead be

= 3 (x*x + x*3 + 3*x + 3*3)

Try to think what the symbols mean..