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8.1: Kuongezea na Kutoa kwa wingi (na Kuchanganya Kama Masharti)

  • Page ID
    164603
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    Ufafanuzi: Kama Masharti

    Ili kuongeza na kuondoa polynomials, kuchanganya kama maneno. Kama maneno na vigezo sawa na exponents sawa. Coefficients ya maneno inaweza kuwa tofauti.

    Kuwa makini wakati wa kuondoa, kusambaza uondoaji (fikiria kama kuongeza\((−1)\) mara nyingi).

    Ongeza au Ondoa Polynomials:

    1. \((−6a^3 + 5a^2 − 7a − 9) + (3a^3 + 5a^2 + a + 8)\)
    2. \((4x^2 − 3) + (3x^2 − 8x + 7)\)
    3. \((3x^2 − 4x + 6) − (2x^2 − x − 9)\)
    4. \((−4x^3 + 5x^2 + 15) − (2x^2 − 4x + 9)\)
    Suluhisho
    1. \(\begin{array} &&(−6a^3+5a^2−7a−9)+(3a^3+5a^2+a+8) &\text{Example problem} \\ &−6a^3 + 3a^3 + 5a^2 + 5a^2 − 7a + a − 9 + 8 &\text{Pair like terms together} \\ &−3a^3 + 10a 2 − 6a − 1 &\text{Solution} \end{array}\)
    1. \(\begin{array} &&(4x^2 − 3) + (3x^2 − 8x + 7) &\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\text{Example problem} \\ &4x^2 + 3x^2 − 8x − 3 + 7 &\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\text{Pair like terms together} \\ &7x^2 − 8x + 4 &\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\text{Solution} \end{array}\)
    1. \(\begin{array} &&(3x^2 − 4x + 6) − (2x^2 − x − 9) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;&\text{Example problem} \\ &3x^2 − 2x^2 − 4x + x + 6 + 9 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;&\text{Distribute the subtraction and pair like terms together} \\ &x^2 − 3x + 15 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;&\text{Solution} \end{array}\)
    1. \(\begin{array} &&(−4x^3 + 5x^2 + 15) − (2x^2 − 4x + 9) \;\;\;\;\;\;\;\;\;\;\;&\text{Example problem} \\ &−4x^3 + 5x^2 − 2x^2 + 4x + 15 − 9 \;\;\;\;\;\;\;\;\;\;\;&\text{Distribute the subtraction and pair like terms together} \\ &−4x^3 + 3x^2 + 4x + 6 \;\;\;\;\;\;\;\;\;\;\;&\text{Solution} \end{array}\)

    Kuongeza au Ondoa Polynomials

    1. \((5x^2 + 8) − (x^2 + 4x + 3)\)
    2. \((x^3 − 14x^2 ) − (−4x^3 + 5x^2 + 8)\)
    3. \((6x^2 + 7x − 9) + (−9x^2 + 2)\)
    4. \((x^3 + 6x^2 − 8x + 14) + (9x^3 − 7x^2 + 5x − 11)\)
    5. \((3x − 4) − (2x^2 − 3x − 9)\)
    6. \((2x^2 + x + 3) − (5x^2 − 1)\)