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Sagot :
Simplifying the given polynomial expression is; -¹/₄x³ - ⁷/₂x² + ²¹⁴/₁₆x + ⁷/₂
How to Simplify Polynomial Expressions?
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
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