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Simplify the polynomial expression. (1/2x +2)(1/2-2x)+(1/4x+7/2)

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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