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Chapter 6: Problem 58

Simplify each algebraic expression. \(2\left(-5 x^{2}+3 x\right)-\left(3 x-5 x^{2}\right)\)

Short Answer

Expert verified
The simplified form of the given algebraic expression is \(-5x^{2} + 3x\).

Step by step solution

01

Distribute the Numbers Outside of the Parentheses

We first distribute the numbers outside the brackets, which are 2 and -1 respectively. Hence, the expression transforms into: \(-10x^{2} + 6x -3x +5x^{2}\).
02

Combine Like Terms

Next, we combine the like terms. 'Like terms' refers to terms that have exactly the same variable parts. In this case, \(-10x^{2}\) and \(5x^{2}\) are like terms as well as \(6x\) and \(-3x\). Combining them gives us: \(-5x^{2} + 3x\).
03

Simplified Form

Thus, the simplified form of the given expression is: \(-5x^{2} + 3x\).

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-25 x-28\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(5 x^{2}-13 x+6\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. It's easy to factor \(x^{2}+x+1\) because of the relatively small numbers for the constant term and the coefficient of \(x\).

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(2 x^{2}+5 x-3\)

Solve each equation using the zero-product principle. \((x+9)(3 x-1)=0\)
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