(7x^3-2x^2) (-2x^2)+(5/4x^2-3x) X-1/2x(x-1)(2x+1)

2 min read Jun 16, 2024

Simplifying Algebraic Expressions

This article will guide you through simplifying the following algebraic expression:

(7x^3 - 2x^2)(-2x^2) + (5/4x^2 - 3x)x - 1/2x(x-1)(2x+1)

We'll break down the process step-by-step, using the distributive property and combining like terms.

We begin by applying the distributive property to each part of the expression:

(7x^3 - 2x^2)(-2x^2):
- (7x^3)(-2x^2) + (-2x^2)(-2x^2) = -14x^5 + 4x^4
(5/4x^2 - 3x)x:
- (5/4x^2)x + (-3x)x = 5/4x^3 - 3x^2
-1/2x(x-1)(2x+1):
- First, we multiply (x-1)(2x+1) = 2x^2 - x - 1
- Then, we multiply -1/2x by the result: -1/2x(2x^2 - x - 1) = -x^3 + 1/2x^2 + 1/2x

Now we combine all the terms we obtained in step 1:

-14x^5 + 4x^4 + 5/4x^3 - 3x^2 - x^3 + 1/2x^2 + 1/2x

Next, we group the terms with the same exponents:

-14x^5 + 4x^4 + (5/4x^3 - x^3) + (-3x^2 + 1/2x^2) + 1/2x

Finally, we combine the coefficients of the like terms:

-14x^5 + 4x^4 + 1/4x^3 - 5/2x^2 + 1/2x

The simplified form of the given algebraic expression is -14x^5 + 4x^4 + 1/4x^3 - 5/2x^2 + 1/2x.