QuestionJuly 15, 2025

Simplify 3(5x^4-2x^2+x)-(4x^3+6x^2-2)

Simplify 3(5x^4-2x^2+x)-(4x^3+6x^2-2)
Simplify 3(5x^4-2x^2+x)-(4x^3+6x^2-2)

Solution
4.6(102 votes)

Answer

15x^4 - 4x^3 - 12x^2 + 3x + 2 Explanation 1. Distribute the 3 Multiply each term inside the parentheses by 3: 3 \times 5x^4, 3 \times (-2x^2), 3 \times x. Result: 15x^4 - 6x^2 + 3x. 2. Distribute the negative sign Distribute the negative sign to each term in the second expression: -(4x^3), -(6x^2), -(-2). Result: -4x^3 - 6x^2 + 2. 3. Combine like terms Add the results from Step 1 and Step 2: (15x^4) + (-4x^3) + (-6x^2 - 6x^2) + (3x) + 2. Simplify: 15x^4 - 4x^3 - 12x^2 + 3x + 2.

Explanation

1. Distribute the 3<br /> Multiply each term inside the parentheses by 3: $3 \times 5x^4$, $3 \times (-2x^2)$, $3 \times x$.<br /> Result: $15x^4 - 6x^2 + 3x$.<br /><br />2. Distribute the negative sign<br /> Distribute the negative sign to each term in the second expression: $-(4x^3)$, $-(6x^2)$, $-(-2)$.<br /> Result: $-4x^3 - 6x^2 + 2$.<br /><br />3. Combine like terms<br /> Add the results from Step 1 and Step 2: $(15x^4) + (-4x^3) + (-6x^2 - 6x^2) + (3x) + 2$.<br /> Simplify: $15x^4 - 4x^3 - 12x^2 + 3x + 2$.
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