Order of operations?

Question

a [ (b^2 + ab) - b^2 ]

a = -2
b= -3

Steps please. =)

Answer 1

start with b^2 = (-3)^2 = 9
ab = -2 x -3 = 6
round parenthesis = (9 + 6) = 15
sq parenthesis 15 - 9 = 6
then x by a
-2 x 6 = -12

Answer 2

You could plug in the numbers, add b^2 to ab first, then subtract b^2, and finally multiply everything by a. But there's a quicker way.

(b^2 + ab) - b^2 is (b^2 + ab) + (-b^2), and since this is all addition, the associate property says you can drop the parentheses. So b^2 + ab + -b^2 simplifies to "ab". This gives you a [ ab ], which is (a*a)b or (a^2)(b).

Now that you have things simplified, you can plug in the numbers to get
(4)(-3) = -12

Again you could start with the original expression and then plug in the numbers and get the same answer. But this other way involves doing less calculations.

Answer 3

PEMDAS (Please Excuse My Dear Aunt Sally) is the order of operations... in other words...
Parenthesis first
Exponents
Multiplication or
Division
Addition or
Subtraction

Solution on left______________ Solved on right
So, a[(b² + ab) - b² ]___________ -2[(-3² + (-2)(-3)) - (-3)² ]
(b)(b) +ab) first _____________ (-3)(-3) +6= 9+6= 15
Then, inside the brackets next
(b)(b)+ab-(b)(b) ______________ 15- (-3)(-3)= 15-9= 6
Then, outside the brackets
a[(b)(b)+ab-(b)(b)]______________ -2[6]
Solve
ab²+a²b-ab²
Answer: a²b ___________________ Answer -12


I gave the solution on the left, and solved on the right. Hope that helps! Another hint... instead of typing ^ to refer to exponents, simply hold ALT and type 0178 for ² and ALT 0179 for ³ .

Answer 4

-2 [ (-3)^2 + -2(-3) - (-3)^2 ]
= -2 [ 9 + 6 - 9 ]
= -2 [ 6 ]
= - 12

Answer 5

a [ (b^2 + ab) - b^2 ]

(-2)[((-3)^2) + (-2)(-3)) - (-3^2)]
(-2)[( 9 + 6 ) - 9]
-2 [ 15 - 9]
-2 [6]
-12

Answer 6

Parenthasees
Exponents
Multplication
Division
Addition
Subtraction
just remember this.... PLEASE EXCUSE MY DEAR AUNT SALLY.