(-2x + 6)(x + 4)

4(13 - 6) - 4^2 + 3^3

For the first problem, you have to use FOIL. And for the second, just use order of operations.

(-2+10)(1+7)

To simplify the expression (-2x + 6)(x + 4), we can use the distributive property. This property states that when we have a product of two expressions, we can distribute each term of the first expression to each term of the second expression. Here's how:

Step 1: Distribute -2x to both terms inside the second parenthesis:
-2x(x + 4) = -2x^2 - 8x

Step 2: Distribute 6 to both terms inside the second parenthesis:
6(x + 4) = 6x + 24

Step 3: Combine the results:
(-2x^2 - 8x) + (6x + 24) = -2x^2 - 8x + 6x + 24

Step 4: Simplify the expression by combining like terms:
-2x^2 - 8x + 6x + 24 = -2x^2 - 2x + 24

Therefore, the simplified form of the expression (-2x + 6)(x + 4) is -2x^2 - 2x + 24.

Moving on to the expression 4(13 - 6) - 4^2 + 3^3:

Step 1: Evaluate the expression inside the parentheses first:
4(13 - 6) = 4(7) = 28

Step 2: Evaluate the exponentiation:
4^2 = 4 x 4 = 16
3^3 = 3 x 3 x 3 = 27

Step 3: Substitute the results back into the expression:
28 - 16 + 27

Step 4: Simplify the expression by performing the addition and subtraction:
28 - 16 + 27 = 12 + 27 = 39

Therefore, the value of the expression 4(13 - 6) - 4^2 + 3^3 is 39.