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.
Similar Questions
- When $x^{4} - px^{3} + 2x^{2} - 5x + 8$ is divided by $x - 1$, the remainder is $2p$. The value of $p$ is:
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Solve the following.
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Important Questions from Polynomials
If (x + y) 3+ 8 (x - y) 3= (3x + Ay) (3x 2+ Bxy + Cy 2), then the value of A + B + C is:
Given that x 8- 34x 4+ 1 = 0, x > 0. What is the value of (x 3+ x -3 )?
If \(x - \frac 3 x = 6,\; x \ne 0,\) then the value of \(\frac {x^4 - \frac {27}{x^2}}{x^2 - 3x - 3}\) is:
If \(x\left(3 - \frac 2 x\right) = \frac 3 x,\) then the value of \(x^3 - \frac 1 {x^3}\) is equal to:
The coefficient of x in (x – 3y) 3is:
