Please confirm if I did the follow problems correctly:
A) Find the sum or difference.
(5a – 3b) + (2a + 6b)= 7a + 9b
Answer: = 7a + 9b
B) Let’s work a few of these (FOIL)
1) (x+2) (x+8) = x 10
Answer: x10
2.) (x+5) (x-7) = x + 11
Answer: x + 11
3.) (2x+4) (2x-3) = 4x + 7
Answer: 4x + 7
A) To find the sum or difference of (5a – 3b) + (2a + 6b), you need to combine like terms. In this case, the like terms are the ones that have the same variable(s).
Step 1: Combine the terms with 'a'. 5a + 2a = 7a.
Step 2: Combine the terms with 'b'. -3b + 6b = 3b.
Therefore, the result of (5a – 3b) + (2a + 6b) is 7a + 3b, not 7a + 9b as you initially stated. So your answer is incorrect.
B) Let's go through each FOIL problem you provided:
1) (x+2) (x+8)
FOIL stands for First, Outer, Inner, Last. Multiply the terms following this pattern.
First: x * x = x^2
Outer: x * 8 = 8x
Inner: 2 * x = 2x
Last: 2 * 8 = 16
Then, combine the results:
x^2 + 8x + 2x + 16 = x^2 + 10x + 16
So your answer for (x+2) (x+8) is correct: x^2 + 10x + 16.
2) (x+5) (x-7)
FOIL:
First: x * x = x^2
Outer: x * -7 = -7x
Inner: 5 * x = 5x
Last: 5 * -7 = -35
Combine the results:
x^2 - 7x + 5x - 35 = x^2 - 2x - 35
So your answer for (x+5) (x-7) is correct: x^2 - 2x - 35.
3) (2x+4) (2x-3)
FOIL:
First: 2x * 2x = 4x^2
Outer: 2x * -3 = -6x
Inner: 4 * 2x = 8x
Last: 4 * -3 = -12
Combine the results:
4x^2 - 6x + 8x - 12 = 4x^2 + 2x - 12
So your answer for (2x+4) (2x-3) is incorrect. The correct answer is 4x^2 + 2x - 12, not 4x + 7.
In summary, you got the first problem wrong but the remaining FOIL problems were correct except for the third one. The correct answer for (2x+4) (2x-3) is 4x^2 + 2x - 12, not 4x + 7.