Question

(1-2x)(1+2x)-(2-x)(2+x)+5(x²-1)-3 ПРЕДСТАВЬТЕ В ВИДЕ МНОГОЧЛЕННА

Answer 1

1-4х^2-4+х^2+5х^2-5-3=2x^2-11

Answer 2

Simplifying the Polynomial Expression

To simplify the given polynomial expression (1-2x)(1+2x)-(2-x)(2+x)+5(x²-1)-3, we can follow the distributive property and combine like terms.

Let's break down the expression step by step:

1. (1-2x)(1+2x) - Using the FOIL method (First, Outer, Inner, Last), we multiply the terms: - (1 * 1) + (1 * 2x) + (-2x * 1) + (-2x * 2x) - Simplifying further, we get: 1 + 2x - 2x - 4x² - Combining like terms, we have: 1 - 4x²

2. (2-x)(2+x) - Again, using the FOIL method, we multiply the terms: - (2 * 2) + (2 * x) + (-x * 2) + (-x * x) - Simplifying further, we get: 4 + 2x - 2x - x² - Combining like terms, we have: 4 - x²

3. 5(x²-1) - Distributing the 5 to both terms inside the parentheses, we get: 5x² - 5

4. Combining all the simplified terms, we have: - (1 - 4x²) - (4 - x²) + (5x² - 5) - 3 - Simplifying further, we get: 1 - 4x² - 4 + x² + 5x² - 5 - 3 - Combining like terms, we have: 2x² + 5x² - 4x² + 1 - 4 - 5 - 3 - Simplifying further, we get: 3x² - 11

Therefore, the simplified form of the given polynomial expression is 3x² - 11.

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