Simplify Algebraic Expression

The goal is to simplify the expression $x(7x - 5) + 3(x^2 - 2) + 14$. This involves using the distributive property and combining like terms.

Step 1: Distribute Terms

Apply the distributive property to the first two parts of the expression:

• $x(7x - 5) = x \times 7x - x \times 5 = 7x^2 - 5x$
• $3(x^2 - 2) = 3 \times x^2 - 3 \times 2 = 3x^2 - 6$

The expression now becomes: $(7x^2 - 5x) + (3x^2 - 6) + 14$.

Step 2: Combine Like Terms

Group terms with the same power of $x$ together:

• Combine the $x^2$ terms: $7x^2 + 3x^2 = 10x^2$
• Combine the $x$ terms: $-5x$ (there's only one term)
• Combine the constant terms: $-6 + 14 = 8$

Step 3: Final Simplified Expression

Combine the results from Step 2 to get the final simplified expression:

$10x^2 - 5x + 8$