Simplify 8m - (2x5m) + 6m + (x+3y)

Question

Asked on March 21, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-21T06:29:10.293Z

Step 1: Expand (5 x - 3 x)^2. (5 x - 3 x)^2 &= 25^2 x - 2·5 x·3 x + 9^2 x \\ &= 25^2 x - 30 x x + 9^2 x Step 2: Expand (3 x + 5 x)^2. (3 x + 5 x)^2 &= 9^2 x + 2·3 x·5 x + 25^2 x \\ &= 9^2 x + 30 x x + 25^2 x Step 3: Add the expansions. &(5 x - 3 x)^2 + (3 x + 5 x)^2 \\ &= (25^2 x - 30 x x + 9^2 x) + (9^2 x + 30 x x + 25^2 x) Step 4: Combine like terms. &= 25^2 x + 9^2 x + 9^2 x + 25^2 x - 30 x x + 30 x x \\ &= 34^2 x + 34^2 x + 0 \\ &= 34(^2 x + ^2 x) Step 5: Use the Pythagorean identity. ^2 x + ^2 x = 1 34(^2 x + ^2 x) = 34 · 1 = 34 Final answer: 34

Accepted Answer · 2026-03-21T06:29:10.293Z

Step 1: Expand (5 x - 3 x)^2. (5 x - 3 x)^2 &= 25^2 x - 2·5 x·3 x + 9^2 x \\ &= 25^2 x - 30 x x + 9^2 x Step 2: Expand (3 x + 5 x)^2. (3 x + 5 x)^2 &= 9^2 x + 2·3 x·5 x + 25^2 x \\ &= 9^2 x + 30 x x + 25^2 x Step 3: Add the expansions. &(5 x - 3 x)^2 + (3 x + 5 x)^2 \\ &= (25^2 x - 30 x x + 9^2 x) + (9^2 x + 30 x x + 25^2 x) Step 4: Combine like terms. &= 25^2 x + 9^2 x + 9^2 x + 25^2 x - 30 x x + 30 x x \\ &= 34^2 x + 34^2 x + 0 \\ &= 34(^2 x + ^2 x) Step 5: Use the Pythagorean identity. ^2 x + ^2 x = 1 34(^2 x + ^2 x) = 34 · 1 = 34 Final answer: 34

Simplify 8m - (2x5m) + 6m + (x+3y)

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Simplify 8m - (2x5m) + 6m + (x+3y)

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