To completely factor 5c^2-24cd-5d^2, I used the following steps: (5c d)(c 5d) to give terms,ignoring signs,5c^2,cd,25cd,5d^2.
+cd-25cd.
(5c+d)(c-5d)
Please correct,if necessary,and show correct way to show this problem.
Thank You.
your solution looks fine
5 c ^ 2 - 24 c d - 5 d ^ 2
Rewrite - 24 c d as - 25 c d + c d
Now:
5 c ^ 2 - 24 c d - 5 d ^ 2 =
5 c ^ 2 - 25 c d + c d - 5 d ^ 2 =
5 c ^ 2 + c d - 25 c d - 5 d ^ 2 =
5 c ^ 2 + c d - ( 25 c d + 5 d ^ 2 ) =
c ( 5 c + d ) - 5 d ( 5 c + d ) =
( 5 c + d ) ( c - 5 d )
Your solution is correct.
To completely factor 5c^2 - 24cd - 5d^2, you need to find two binomials that, when multiplied together, give you the original expression.
First, let's ignore the signs and write all the possible ways to factor 5c^2 and 5d^2:
5c^2: (5c)(c), (-5c)(-c), (1c)(5c), (-1c)(-5c)
5d^2: (5d)(d), (-5d)(-d), (1d)(5d), (-1d)(-5d)
Next, we need to consider the combination of these factors that will give us the middle term, -24cd.
We observe that the only combination that can give us -24cd is:
(-5c)(5d) + (1c)(-1d) = -25cd + cd = -24cd.
So the correct factored form of 5c^2 - 24cd - 5d^2 is (5c - d)(c + 5d).
To verify this, you can use the distributive property to multiply (5c - d)(c + 5d) and check if it gives you the original expression, 5c^2 - 24cd - 5d^2.