Question
Simplify: $x(2x - 3) + 2(x^2 - 4) + 16$
This question was previously asked in
RRB NTPC 2024 CBT 1 Question Paper (28-Aug-2025) (Shift 3)
The correct answer is
$4x^2 - 3x + 8$
Algebra Simplification: Step-by-Step Solution
The problem asks us to simplify the algebraic expression: $x(2x - 3) + 2(x^2 - 4) + 16$. We will use the distributive property and combine like terms.
Step-by-step Solution
- Distribute the $x$ in the first term: $x(2x - 3) = x \cdot 2x - x \cdot 3 = 2x^2 - 3x$.
- Distribute the $2$ in the second term: $2(x^2 - 4) = 2 \cdot x^2 - 2 \cdot 4 = 2x^2 - 8$.
- Now, substitute these expanded terms back into the original expression: $(2x^2 - 3x) + (2x^2 - 8) + 16$.
- Group like terms together: Combine the $x^2$ terms: $2x^2 + 2x^2$. Combine the $x$ terms: $-3x$. Combine the constant terms: $-8 + 16$.
- Simplify by performing the addition and subtraction: $2x^2 + 2x^2 = 4x^2$. The expression becomes $4x^2 - 3x + (-8 + 16)$. $-8 + 16 = 8$.
- The final simplified expression is $4x^2 - 3x + 8$.
The simplified expression matches Option 1.
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