8(a-b)2+14(a-b)-15
Is 8(a-b)2 supposed to mean 8(a-b)^2?
If so, what you have written can be factored into
[2(a-b)+ 5][4(a-b)-3]
= (2a -2b +5)(4a -4b -3)
Yes, based on the assumption that 8(a-b)2 means 8(a-b)^2, we can simplify the expression.
To factor the expression, we can use the distributive property to expand it first:
8(a-b)^2 + 14(a-b) - 15
Now, let's focus on factoring the terms that involve (a-b) separately.
For the first term, 8(a-b)^2, we can use the formula (a-b)^2 = a^2 - 2ab + b^2 to expand it:
8(a^2 - 2ab + b^2)
This gives us: 8a^2 - 16ab + 8b^2
Now, let's combine this with the other terms:
8a^2 - 16ab + 8b^2 + 14(a-b) - 15
Next, we can further simplify it:
8a^2 - 16ab + 8b^2 + 14a - 14b - 15
Now, we can regroup the terms:
(8a^2 + 14a) + (-16ab - 14b) + (8b^2 - 15)
Now, let's factor out common factors from each group:
2a(4a + 7) - 2b(8a + 7) + (8b^2 - 15)
Now, we can see that (4a + 7) and (8a + 7) are common factors in the first two terms. Similarly, (8b^2 - 15) is not factorable further.
So, the final factored form is:
(4a + 7)(2a - 2b) + (8b^2 - 15)
Therefore, the factored form of the expression 8(a-b)^2 + 14(a-b) - 15 is (4a + 7)(2a - 2b) + (8b^2 - 15).