Examkin

Question

Difficulty: Very hardSimplifying Algebraic Expressions

Which of the following is equivalent to the expression below?

2x(3x−4)−3[x(x−2)−4(2x+1)]+x22x(3x - 4) - 3[x(x - 2) - 4(2x + 1)] + x^2
  1. 4x2+22x+124x^2 + 22x + 12Answer
  2. B
    4x2−38x−124x^2 - 38x - 12
  3. C
    4x2+34x4x^2 + 34x
  4. D
    4x2−18x−44x^2 - 18x - 4

Answer

The correct expression is 4x2+22x+124x^2 + 22x + 12.
The correct expression is found by following the order of operations: first expanding the terms inside the innermost parentheses, then combining like terms within the brackets, next distributing the negative multiplier to all terms in the brackets, and finally combining all remaining like terms.

Step-by-Step Solution

1
Expand the first part of the expression by distributing 2x2x.
2x(3x−4)=6x2−8x2x(3x - 4) = 6x^2 - 8x
Distribution is required to remove the initial parentheses.
2
Simplify the expression inside the square brackets by distributing and combining like terms.
x(x−2)−4(2x+1)=x2−2x−8x−4=x2−10x−4x(x - 2) - 4(2x + 1) = x^2 - 2x - 8x - 4 = x^2 - 10x - 4
According to the order of operations, simplify the innermost grouping symbols first.
3
Distribute the −3-3 across the simplified expression from the brackets.
−3(x2−10x−4)=−3x2+30x+12-3(x^2 - 10x - 4) = -3x^2 + 30x + 12
The negative sign and the constant must be multiplied by every term inside the brackets.
4
Substitute all parts back into the main expression and combine like terms.
(6x2−8x)+(−3x2+30x+12)+x2=(6x2−3x2+x2)+(−8x+30x)+12=4x2+22x+12(6x^2 - 8x) + (-3x^2 + 30x + 12) + x^2 = (6x^2 - 3x^2 + x^2) + (-8x + 30x) + 12 = 4x^2 + 22x + 12
Combining coefficients of terms with the same variables and exponents yields the final simplified polynomial.

Key Concept

Simplifying complex algebraic expressions by applying the distributive property, handling negative multipliers, and combining like terms.
Rate this question

Topics

Simplifying Algebraic Expressions

More questions from this topic