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Zorluk: ZorSimplifying Expressions and Combining Like Terms

When the expression 6x−2x(x−3y)−(2x−12y)2−34x(6x−8)6x - 2x(x - 3y) - \left(2x - \frac{1}{2}y\right)^2 - \frac{3}{4}x(6x - 8) is simplified by combining like terms, what is the coefficient of the x2x^2 term?

  1. A
    −92-\frac{9}{2}
  2. B
    -5
  3. C
    -6
  4. D
    −172-\frac{17}{2}
  5. −212-\frac{21}{2}Cevap

Cevap

−212-\frac{21}{2}
Expanding the entire expression yields the x2x^2 terms −2x2-2x^2, −4x2-4x^2, and −92x2-\frac{9}{2}x^2. Summing these coefficients gives −2−4−92=−212-2 - 4 - \frac{9}{2} = -\frac{21}{2}. Therefore, the coefficient of the x2x^2 term is −212-\frac{21}{2}.

Adım Adım Çözüm

1
Expand the first parenthetical expression by distributing the term −2x-2x.
−2x(x−3y)=−2x2+6xy-2x(x - 3y) = -2x^2 + 6xy. The expression becomes: 6x−2x2+6xy−(2x−12y)2−34x(6x−8)6x - 2x^2 + 6xy - \left(2x - \frac{1}{2}y\right)^2 - \frac{3}{4}x(6x - 8).
Distribution is required to eliminate parentheses before terms can be combined.
2
Expand the squared binomial (2x−12y)2\left(2x - \frac{1}{2}y\right)^2 using the identity (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2, then distribute the negative sign.
(2x−12y)2=4x2−2xy+14y2\left(2x - \frac{1}{2}y\right)^2 = 4x^2 - 2xy + \frac{1}{4}y^2. Distributing the negative gives −4x2+2xy−14y2-4x^2 + 2xy - \frac{1}{4}y^2.
This simplifies the second parenthetical term of the expression.
3
Expand the third parenthetical term by distributing −34x-\frac{3}{4}x.
−34x(6x−8)=−92x2+6x-\frac{3}{4}x(6x - 8) = -\frac{9}{2}x^2 + 6x.
This simplifies the final parenthetical term of the expression.
4
Combine the coefficients of all the x2x^2 terms.
The x2x^2 terms are −2x2-2x^2, −4x2-4x^2, and −92x2-\frac{9}{2}x^2. Combining their coefficients gives: −2−4−92=−6−92=−122−92=−212-2 - 4 - \frac{9}{2} = -6 - \frac{9}{2} = -\frac{12}{2} - \frac{9}{2} = -\frac{21}{2}.
Combining like terms simplifies the expression to find the final coefficient of x2x^2.

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Simplifying algebraic expressions by distributing coefficients and combining like terms.
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Simplifying Expressions and Combining Like Terms

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