Problems 1, 2, and 3: I'm not sure I can rewrite these correctly, so I'll answer generally. It looks like each of these involve the order of operations, which is:
Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right).
So if problem 1 is 8 divided by 2 times 2 minus 3 to the 2nd power,
this would look like 8 ÷ 2 * 2 - 32
By order of operations, we do the exponents (32) first, and we get
8 ÷ 2 * 2 - 9
Now we do multiplication and division as we encounter them from left to right. So first we tackle 8 ÷ 2 and rewrite our expression with the result
4 * 2 - 9
Now we have 4 * 2 (which equals 8), and we rewrite our expression again:
8 - 9
Now, there is nothing left but subtraction, and 8-9 = -1.
Given that explanation, see if you can apply this process to problems 2 and 3
You can remember the order of operations with the saying "Please Excuse My Dear Aunt Sally":
Please = Parentheses
Excuse = Exponents
My = Multiplication
Dear = Division
Aunt = Addition
Sally = Subtraction
Problem 4: If x = -3, then 4x2 - 3x - 10 = ?
Replace x in the expression with (-3), to get
4(-3)2 - 3(-3) - 10 = 4(9) + 9 - 10 = (I'll leave the final answer for you)
Problem 5: Since the board is cut into two pieces, let's let x = length of first piece and y = length of second piece. We then know that x + y = 8 feet
Since one piece is 2 feet longer than the other, let's assume that the first piece is longer than the second, so we now have a second equation, x = y + 2
Replace x in the first equation with y+2 (from the second equation), and we now have
(y+2) + y = 8
2y + 2 = 8
2y = 6
y = 3 . Since we assumed that y was the shorter board, this is our answer.
Problem 6: I'm reading this as (3x2y)(2x3y).
If so, we multiply common factors together:
(3*2)(x2x3)(yy) = 6 x2+3y1+1 =
Problem 7: If looks like the problem is 5a3 - 2a2 - (4a2 - 3). If so, then your answer is close, with one change:
The negative in front of (4a2 - 3) gets distributed across both terms within the parentheses. So if we cleared the parens, our expression would look like
5a3 - 2a2 + (-1)( 4a2) + (-1)(- 3) = 5a3 - 6a2