Simplify by using factoring:(2a+6b)(6b−2a)−(2a+6b)^2
Thanks for helping!
Notice that (2a + 6b) is a common factor, so ...
(2a+6b)( (6b-2a) - (2a+6b) )
simplify the inside of my outside brackets and you are done
by the way, I only did step one.
But wouldn't (6b-2a) already be there? how could you group it?
the square is outside the parentheses
6 = 2*3
To simplify the given expression (2a+6b)(6b−2a)−(2a+6b)^2, we can break it down into steps:
Step 1: Expand the first two terms.
(2a+6b)(6b−2a) = 2a * 6b + 2a * (-2a) + 6b * 6b + 6b * (-2a)
Simplifying, we get:
12ab - 4a^2 + 36b^2 - 12ab
Step 2: Combine like terms.
12ab - 12ab is equal to 0, so it cancels out.
Simplifying further, we have:
-4a^2 + 36b^2
Step 3: Simplify the last term.
(2a+6b)^2 = (2a+6b)(2a+6b) = 4a^2 + 12ab + 12ab + 36b^2
Simplifying, we get:
4a^2 + 24ab + 36b^2
Step 4: Subtract the last term from the expression.
-4a^2 + 36b^2 - (4a^2 + 24ab + 36b^2)
When subtracting, distribute the negative sign to each term inside the parentheses:
-4a^2 + 36b^2 - 4a^2 - 24ab - 36b^2
Simplifying further, we have:
-8a^2 - 24ab
Thus, the simplified form of (2a+6b)(6b−2a)−(2a+6b)^2 is -8a^2 - 24ab.
(2a+6b) [ 6b -2a -2a - 6b ]
-4a (2a+6b)