QuestionAugust 25, 2025

Find the product and simplify. (x^2-2x-4)(x^2-3x-5)= square

Find the product and simplify. (x^2-2x-4)(x^2-3x-5)= square
Find the product and simplify. (x^2-2x-4)(x^2-3x-5)= square

Solution
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Answer

x^4 - 5x^3 - 3x^2 + 22x + 20 Explanation 1. Expand the expression Use the distributive property to expand: (x^2 - 2x - 4)(x^2 - 3x - 5) = x^2(x^2 - 3x - 5) - 2x(x^2 - 3x - 5) - 4(x^2 - 3x - 5). 2. Distribute each term Calculate each part: - x^2(x^2 - 3x - 5) = x^4 - 3x^3 - 5x^2, - -2x(x^2 - 3x - 5) = -2x^3 + 6x^2 + 10x, - -4(x^2 - 3x - 5) = -4x^2 + 12x + 20. 3. Combine like terms Add all parts together: x^4 - 3x^3 - 5x^2 - 2x^3 + 6x^2 + 10x - 4x^2 + 12x + 20. Simplify by combining like terms: x^4 - 5x^3 - 3x^2 + 22x + 20.

Explanation

1. Expand the expression<br /> Use the distributive property to expand: $(x^2 - 2x - 4)(x^2 - 3x - 5) = x^2(x^2 - 3x - 5) - 2x(x^2 - 3x - 5) - 4(x^2 - 3x - 5)$.<br />2. Distribute each term<br /> Calculate each part: <br />- $x^2(x^2 - 3x - 5) = x^4 - 3x^3 - 5x^2$,<br />- $-2x(x^2 - 3x - 5) = -2x^3 + 6x^2 + 10x$,<br />- $-4(x^2 - 3x - 5) = -4x^2 + 12x + 20$.<br />3. Combine like terms<br /> Add all parts together: $x^4 - 3x^3 - 5x^2 - 2x^3 + 6x^2 + 10x - 4x^2 + 12x + 20$.<br /> Simplify by combining like terms: $x^4 - 5x^3 - 3x^2 + 22x + 20$.
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