Get expert advice and community support for all your questions on IDNLearn.com. Our platform offers reliable and comprehensive answers to help you make informed decisions quickly and easily.
Simplifying the given polynomial expression is; -¹/₄x³ - ⁷/₂x² + ²¹⁴/₁₆x + ⁷/₂
We want to simplify the polynomial expression;
(¹/₂x + 2)(¹/₂ - 2x) + (¹/₄x + ⁷/₂)
Let us expand the first bracket to get;
((¹/₂x * ¹/₂) + (2 * ¹/₂) - (¹/₂x * 2x) - (2 * 2x))
⇒ ¹/₄x + 1 - x² - 4x
⇒ 1 + ¹⁵/₄x - x²
Thus, our expression is now;
(1 + ¹⁵/₄x - x²)(¹/₄x + ⁷/₂)
This can be multiplied out to give;
¹/₄x + ¹⁵/₁₆x - ¹/₄x³ + ⁷/₂ + ¹⁰⁵/₈x - ⁷/₂x²
= -¹/₄x³ - ⁷/₂x² + ¹⁰⁷/₈x + ¹⁵/₁₆x + ⁷/₂
= -¹/₄x³ - ⁷/₂x² + ²¹⁴/₁₆x + ⁷/₂
Read more about Simplifying Polynomial Expressions at; https://brainly.com/question/723406
#SPJ1