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2015-09-26T18:10:31+08:00

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P = 4x⁴ - 3x³ + x² - 5x + 11
Q = -3x⁴ + 6x³ - 8x² + 4x - 3

2P + Q = 5x⁴ - 6x² - 6x + 19

Substitute the values of P and Q.
2 (4x⁴ - 3x³ + x² - 5x + 11) + (-3x⁴ + 6x³ - 8x² + 4x - 3)

Multiply 2 by (4x⁴ - 3x³ + x² - 5x + 11) using the distributive property of multiplication.
(2 · 4x⁴) + (2 · -3x³) + (2 · x²) + (2 · -5x) + (2 · 11) + (-3x⁴ + 6x³ - 8x² + 4x - 3)
(8x⁴ - 6x³ + 2x² - 10x + 22) + (-3x⁴ + 6x³ - 8x² + 4x - 3)

Combine like terms together.
(8x⁴ + -3x⁴) + (6x³ 6x³) + (2x² + -8x²) + (-10x 4x(22 + -3)
5x
⁴ + 0 + - 6x² - 6x + 19
5x⁴ - 6x² - 6x + 19

P - 2Q = 10x⁴ - 15x³ + 17x² - 13x + 17

Substitute values of P and Q
(4x⁴ - 3x³ + x² - 5x + 11) - 2 (-3x⁴ + 6x³ - 8x² + 4x - 3)

Multiply using the distributive property of multiplication.
(4x⁴ - 3x³ + x² - 5x + 11) + (-2 · -3x⁴) + (-2 · 6x³) + (-2 · -8x²) + (-2 · 4x) + (-2 · -3)
(4x⁴ - 3x³ + x² - 5x + 11) + (6x⁴ - 12x³ + 16x² - 8x + 6)

Combine like terms.
(4x⁴ + 6x⁴) + (-3x³ + -12x³) + (x² + 16x²) + (-5x + - 8x) + (11 + 6)
10x⁴ - 15x³ + 17x² - 13x + 17
 
                                                                          -KookEin
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