%5E2%2B2a-6b.jpeg "(a-3b)^2+2a-6b")
Expanding and Simplifying the Expression: (a-3b)^2 + 2a - 6b
This expression involves both squaring a binomial and combining like terms. Let's break it down step by step.
Step 1: Expanding the Squared Binomial
The term (a-3b)^2 represents the product of (a-3b) multiplied by itself. We can use the FOIL method (First, Outer, Inner, Last) to expand this:
(a-3b)^2 = (a-3b)(a-3b) = a^2 - 3ab - 3ab + 9b^2 = a^2 - 6ab + 9b^2
Step 2: Combining Like Terms
Now our expression looks like this: a^2 - 6ab + 9b^2 + 2a - 6b
We can group the like terms together:
a^2 + 2a - 6ab - 6b + 9b^2
Step 3: Simplified Expression
The final simplified expression is: a^2 + 2a - 6ab - 6b + 9b^2
This is the expanded and simplified form of the original expression (a-3b)^2 + 2a - 6b.
Note: This expression cannot be further simplified as there are no more like terms.