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1.1.3 Qulz: Algebraic Expressions
Question 6 of 10
Which expression is the simplest form of 
-(4x^(3)+x^(2))+2(x^(3)-3x^(2))?
A. 
-6x^(3)-2x^(2)
B. 
-2x^(3)-5x^(2)
C. 
-2x^(3)-7x^(2)
D. 
-6x^(3)-6x^(2)
SUBMIT
PREVIOUS

11.11.33 Qulz: Algebraic Expressions\newlineQuestion 66 of 1010\newlineWhich expression is the simplest form of (4x3+x2)+2(x33x2)? -\left(4 x^{3}+x^{2}\right)+2\left(x^{3}-3 x^{2}\right) ? \newlineA. 6x32x2 -6 x^{3}-2 x^{2} \newlineB. 2x35x2 -2 x^{3}-5 x^{2} \newlineC. 2x37x2 -2 x^{3}-7 x^{2} \newlineD. 6x36x2 -6 x^{3}-6 x^{2} \newlineSUBMIT\newlinePREVIOUS

Full solution

Q. 11.11.33 Qulz: Algebraic Expressions\newlineQuestion 66 of 1010\newlineWhich expression is the simplest form of (4x3+x2)+2(x33x2)? -\left(4 x^{3}+x^{2}\right)+2\left(x^{3}-3 x^{2}\right) ? \newlineA. 6x32x2 -6 x^{3}-2 x^{2} \newlineB. 2x35x2 -2 x^{3}-5 x^{2} \newlineC. 2x37x2 -2 x^{3}-7 x^{2} \newlineD. 6x36x2 -6 x^{3}-6 x^{2} \newlineSUBMIT\newlinePREVIOUS
  1. Distribute negative sign: First, distribute the negative sign to the terms inside the first set of parentheses: 1×(4x3+x2)=4x3x2-1 \times (4x^3 + x^2) = -4x^3 - x^2.
  2. Distribute 22: Next, distribute the 22 to the terms inside the second set of parentheses: 2×(x33x2)=2x36x22 \times (x^3 - 3x^2) = 2x^3 - 6x^2.
  3. Combine like terms: Now, combine like terms by adding the results from the first two steps: (4x3x2)+(2x36x2)=4x3+2x3x26x2(-4x^3 - x^2) + (2x^3 - 6x^2) = -4x^3 + 2x^3 - x^2 - 6x^2.
  4. Simplify expression: Simplify the expression by combining the x3x^3 terms and the x2x^2 terms: 4x3+2x3=2x3-4x^3 + 2x^3 = -2x^3 and x26x2=7x2-x^2 - 6x^2 = -7x^2.
  5. Final simplified expression: Write the final simplified expression: 2x37x2-2x^3 - 7x^2.

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