Simplifying the Algebraic Expression
The task is to simplify the given algebraic expression: $x(7x - 2) + 5(x^2 - 3) + 13$
Step-by-Step Simplification
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Apply the distributive property to the first term, $x(7x - 2)$: $x \times 7x - x \times 2 = 7x^2 - 2x$
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Apply the distributive property to the second term, $5(x^2 - 3)$: $5 \times x^2 - 5 \times 3 = 5x^2 - 15$
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Substitute the expanded terms back into the original expression: $(7x^2 - 2x) + (5x^2 - 15) + 13$
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Group the like terms together: terms with $x^2$, terms with $x$, and constant terms. $(7x^2 + 5x^2) + (-2x) + (-15 + 13)$
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Combine the coefficients of the like terms: $12x^2 - 2x - 2$
Final Answer
The simplified expression is $12x^2 - 2x - 2$. This matches the third option.
Similar Questions
Simplify: $3((\frac{5}{3})x^2 - 28x + 15) - 5(x^2 + 6x - 15)$
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
