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Addition of Polynomials

Simplify:i 3 ...

Question

Simplify:

(i) (3x² $-$ 2x + 1) + (x² + 5x $-$ 3) + (4x² + 8)
(ii) (2y³ + 3y $-$ 7) $-$ (8y $-$ 6) + (4y³ $-$ 2y + 1)
(iii) 5m³ $-$ m + 6m² $-$ (3m² $-$ 2 + m)

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Solution

$(i) (3 x^{2} - 2 x + 1) + (x^{2} + 5 x - 3) + (4 x^{2} + 8) = 3 x^{2} - 2 x + 1 + x^{2} + 5 x - 3 + 4 x^{2} + 8 = 3 x^{2} + x^{2} + 4 x^{2} - 2 x + 5 x + 1 - 3 + 8 = 8 x^{2} + 3 x + 6$

$(ii) (2 y^{3} + 3 y - 7) - (8 y - 6) + (4 y^{3} - 2 y + 1) = 2 y^{3} + 3 y - 7 - 8 y + 6 + 4 y^{3} - 2 y + 1 = 2 y^{3} + 4 y^{3} + 3 y - 8 y - 2 y - 7 + 6 + 1 = 6 y^{3} - 7 y$

$(iii) 5 m^{3} - m + 6 m^{2} - (3 m^{2} - 2 + m) = 5 m^{3} - m + 6 m^{2} - 3 m^{2} + 2 - m = 5 m^{3} + 6 m^{2} - 3 m^{2} - m - m + 2 = 5 m^{3} + 3 m^{2} - 2 m + 2$

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Similar questions

(2 y^{3} + 3 y - 7) - (8 y - 6) + (4 y^{3} - 2 y + 1)

5 m^{3} - m + 6 m^{2} - (3 m^{2} - 2 + m)

Q. Factorize the following polynomials.
(i) (x² – x)² – 8 (x² – x) + 12
(ii) (x – 5)² – (5x – 25) – 24
(iii) (x² – 6x)² – 8 (x² – 6x + 8) – 64
(iv) (x² – 2x + 3) (x² – 2x + 5) – 35
(v) (y + 2) (y – 3) (y + 8) (y + 3) + 56
(vi) (y² + 5y) (y² + 5y – 2) – 24
(vii) (x – 3) (x – 4)² (x – 5) – 6

(3 x^{2} - 2 x + 1) + (x^{2} + 5 x - 3) + (4 x^{2} + 8)

(3 x^{2} - \frac{1}{5} x + \frac{7}{3}) + (- \frac{1}{4} x^{2} + \frac{1}{3} x + \frac{1}{3} x - \frac{1}{6}) + (- 2 x^{2} - \frac{1}{2} x + 5)

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