Simplify Algebraic Expression Step-by-Step

To simplify the given algebraic expression $x(3x - 8) + 3(x^2-5) + 11$, we need to follow the order of operations and combine like terms.

Distribute Terms

First, apply the distributive property to the terms in parentheses:

• Distribute $x$ into $(3x - 8)$: $x \cdot (3x - 8) = (x \cdot 3x) - (x \cdot 8) = 3x^2 - 8x$
• Distribute $3$ into $(x^2 - 5)$: $3 \cdot (x^2 - 5) = (3 \cdot x^2) - (3 \cdot 5) = 3x^2 - 15$

Combine Expanded Terms

Now, substitute these expanded forms back into the original expression:

Remove the parentheses:

Combine Like Terms

Next, group the like terms together. Like terms are terms that have the same variable raised to the same power.

• Combine the $x^2$ terms: $3x^2 + 3x^2$
• Combine the $x$ terms: $-8x$ (there is only one $x$ term)
• Combine the constant terms: $-15 + 11$

Perform the combinations:

• $3x^2 + 3x^2 = 6x^2$
• The $x$ term remains $-8x$
• $-15 + 11 = -4$

Final Simplified Expression

Putting it all together, the simplified expression is:

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