Question

The sum of three algebraic expressions is 2x3– 5x2. If two of the expressions are x3 – x2 and 4x2 – x3, find the third.​

Answer 1

Here, given that the sum of three algebraic expressions is 2x³ - 5x².

Two of the expressions are-

• x³ - x²
• 4x² - x³

Let the third expression be y. Then,

=> (x³ - x²) + (4x² - x³) + y = 2x³ - 5x²

=> (x³ - x² + 4x² - x³ )+ y = (2x³ - 5x² )

• Place the sum of (x³ - x²) and (4x²- x³) together

=> y = (2x³ - 5x²) - (x³ - x² + 4x² - x³)

=> y = 2x³ - 5x² - x³ + x² - 4x² + x³

=> y = 2x³ + x³ - x³ - 5x² + x² - 4x²

=> y = 2x³ - 4x² - 4x²

=> y = 2x³ - 8x²

Verification -

=> (x³ - x²) + (4x² - x³) + (2x³ - 8x²) = 2x³ - 5x²

=> x³ - x² + 4x² - x³ + 2x³ - 8x² = 2x³ - 5x²

=> x³ - x³ + 2x³ - 8x² - x² + 4x² = 2x³ - 5x²

=> 2x³ - 8x² + 3x² = 2x³ - 5x²

=> 2x³ - 5x² = 2x³ - 5x²

∴Hence, the third expression is 2x³ - 8x²