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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- Select the term that can replace the question mark (?) in the following equation.
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Important Questions from Algebric Equations
A group of 630 children is seated in rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible?
The letters L, M, N, 0, P, Q, R, S and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3.
What is the integer assigned to N?
Four persons, Alok, Bhupesh, Chander and Dinesh have a total of Rs. 100 among themselves. Alok and Bhupesh between them have as much money as Chander and Dinesh between them, but Alok has more money than Bhupesh; and Chander has only half the money that Dinesh has. Alok has in fact Rs. 5 more than Dinesh has.
Who has the maximum amount of money?
If x=3/2, then the value of 27x3-54x2+36x-11 is
If a+b+c = 6 and ab+bc+ca = 11, then the value of bc(b+c) + ca(c+a) +ab(a+b) +3abc is
