4%2F(5a-4b-5)-2.jpeg "(5a3b-2)4/(5a-4b-5)-2")
Simplifying Algebraic Expressions: (5a3b-2)4/(5a-4b-5)-2
Algebraic expressions can be intimidating, but with the right techniques, we can simplify them and make them easier to work with. In this article, we'll explore how to simplify the expression (5a3b-2)4/(5a-4b-5)-2.
Step 1: Expand the Expression
To start, let's expand the expression using the distributive property:
(5a3b-2)4 = 5a3b*4 - 2*4 = 20a3b - 8
Next, let's expand the denominator:
5a - 4b - 5 = (5a - 4b) - 5
Now we can rewrite the original expression:
(20a3b - 8) / ((5a - 4b) - 5) - 2
Step 2: Simplify the Fraction
To simplify the fraction, we can try to find common factors between the numerator and denominator. Let's start by factoring out the greatest common factor (GCF) of the numerator:
20a3b - 8 = 4(5a3b - 2)
Now, let's rewrite the expression with the factored numerator:
(4(5a3b - 2)) / ((5a - 4b) - 5) - 2
Step 3: Cancel Out Terms
Next, we can try to cancel out terms between the numerator and denominator. Let's see if we can find a common factor:
5a - 4b - 5 = (5a - 4b) - 5
Hmm, it looks like we can factor out a -1 from the denominator:
(5a - 4b) - 5 = -(5 - 5a + 4b)
Now we can rewrite the expression with the factored denominator:
(4(5a3b - 2)) / -(5 - 5a + 4b) - 2
Step 4: Simplify Further
Finally, we can try to simplify the expression further by combining like terms:
(4(5a3b - 2)) / -(5 - 5a + 4b) - 2 = (20a3b - 8) / (5a - 4b - 5) - 2
And that's it! We've simplified the expression (5a3b-2)4/(5a-4b-5)-2 to (20a3b - 8) / (5a - 4b - 5) - 2.
By following these steps, we've simplified the expression and made it easier to work with. Remember to always follow the order of operations (PEMDAS) and to look for common factors and terms to cancel out. Happy simplifying!
