(2a-4)-(2a-5)2-3(4a-12).jpeg "(3a+2)(2a-4)-(2a-5)2 3(4a-12)")
Expanding and Simplifying Algebraic Expressions
In this article, we will explore how to expand and simplify algebraic expressions, specifically focusing on the expression (3a+2)(2a-4)-(2a-5)2 and its equivalent form 3(4a-12).
Expanding the Expression
Let's start by expanding the given expression (3a+2)(2a-4)-(2a-5)2.
(3a+2)(2a-4)
Using the distributive property, we can expand the expression as:
(3a+2)(2a-4) = 3a(2a-4) + 2(2a-4)
= 6a² - 12a + 4a - 8
= 6a² - 8a - 8
-(2a-5)2
Now, let's expand the second part of the expression:
-(2a-5)2 = -(4a² - 20a + 25)
= -4a² + 20a - 25
Combining the Expanded Expressions
Now that we have expanded both parts of the expression, we can combine them:
(3a+2)(2a-4)-(2a-5)2 = 6a² - 8a - 8 - (-4a² + 20a - 25)
= 6a² - 8a - 8 + 4a² - 20a + 25
= 10a² - 28a + 17
Equivalent Form: 3(4a-12)
Now, let's see how this expression is equivalent to 3(4a-12).
3(4a-12) = 3(4a) - 3(12)
= 12a - 36
So, we can see that the two expressions (3a+2)(2a-4)-(2a-5)2 and 3(4a-12) are equivalent.
In conclusion, we have successfully expanded and simplified the algebraic expression (3a+2)(2a-4)-(2a-5)2 and shown its equivalence to 3(4a-12).
