%5E2-4a(a-6b).jpeg "(2a-3b)^2-4a(a-6b)")
Simplifying the Expression: (2a-3b)^2 - 4a(a-6b)
This article will guide you through simplifying the algebraic expression (2a-3b)^2 - 4a(a-6b). We will use the order of operations (PEMDAS/BODMAS) and algebraic properties to achieve a simplified form.
Step 1: Expanding the Square
First, we need to expand the square term (2a-3b)^2. Remember that squaring a binomial means multiplying it by itself:
(2a-3b)^2 = (2a-3b) * (2a-3b)
We can use the FOIL method (First, Outer, Inner, Last) to multiply these binomials:
(2a-3b) * (2a-3b) = 4a^2 - 6ab - 6ab + 9b^2 = 4a^2 - 12ab + 9b^2
Step 2: Expanding the Second Term
Next, we distribute the -4a to the terms inside the parentheses:
-4a(a-6b) = -4a * a + (-4a) * (-6b) = -4a^2 + 24ab
Step 3: Combining Like Terms
Now, we have the expression in the following form:
4a^2 - 12ab + 9b^2 - 4a^2 + 24ab
We can combine the like terms:
4a^2 - 4a^2 - 12ab + 24ab + 9b^2 = 12ab + 9b^2
Final Result
Therefore, the simplified form of the expression (2a-3b)^2 - 4a(a-6b) is 12ab + 9b^2.