How would I simplify the following, but leave it in factored form?
[(2x+7)^6 x 5(x-2)^4] + [(x-2)^5 x 6(2x+7)^5 x 2]
If you can also explain how to do it step by step, that would be VERY appreciated. THANK YOU SO MUCH.
See reply to your 6:51pm posting below.
((2x^7)^5 x (x-2)^4)*[12(x-2)]
To simplify the expression [(2x+7)^6 x 5(x-2)^4] + [(x-2)^5 x 6(2x+7)^5 x 2] and leave it in factored form, follow these step-by-step instructions:
Step 1: Identify like terms
Look at the expression and identify terms that have the same base raised to the same exponent. In this case, the terms (2x+7)^6 and (2x+7)^5 have the same base, and the terms (x-2)^4 and (x-2)^5 also have the same base.
Step 2: Distribute coefficients
Distribute the coefficients (5 and 6) to the terms within parentheses separately. This will give you two separate terms:
[(2x+7)^6 x 5(x-2)^4] + [(x-2)^5 x 6(2x+7)^5 x 2]
= (5 x (2x+7)^6 x (x-2)^4) + (6 x (x-2)^5 x (2x+7)^5 x 2)
Step 3: Combining like terms
Now that the coefficients have been distributed, you can combine the like terms. In the first term, the common factor is (2x+7)^6, and in the second term, the common factor is (x-2)^5. Pull out these common factors:
= (2x+7)^6 x [(5 x (x-2)^4) + (6 x 2(2x+7)^5)]
Step 4: Simplify the coefficients
Simplify the coefficients within the brackets:
= (2x+7)^6 x [(5x-10)^4 + 12(2x+7)^5]
Step 5: Combining like terms (again)
Now, within the brackets, we have two terms. The common factor is (2x+7)^5. Pull that out:
= (2x+7)^6 x ([(5x-10)^4 + 12] x (2x+7)^5)
This is the factored form of the simplified expression.