Problem 25
Question
Find each product. $$(2 x-3)(5 x+3)$$
Step-by-Step Solution
Verified Answer
The product is \(10x^2 -9x - 9\).
1Step 1: Distribute the first term of the first binomial
Multiply the first term of the first binomial, \(2x\), with each term of the second binomial, \(5x\) and \(3\). This results in: \(10x^2\) and \(6x\). The expression becomes: \(10x^2 + 6x\).
2Step 2: Distribute the second term of the first binomial
Multiply the second term of the first binomial, \(-3\), with each term of the second binomial, \(5x\) and \(3\). This yields: \(-15x\) and \(-9\). The expression now is: \(10x^2 + 6x -15x -9\).
3Step 3: Combine Like Terms
Combine the like terms \(6x\) and \(-15x\) to simplify the expression. This yields: \(10x^2 -9x - 9\).
Other exercises in this chapter
Problem 25
Multiply or divide as indicated. $$\frac{x^{2}-4}{x} \div \frac{x+2}{x-2}$$
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Factor each trinomial, or state that the trinomial is prime. $$ 3 x^{2}-25 x-28 $$
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Simplify each exponential expression in Exercises 23–64. $$x^{0} y^{5}$$
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Use the quotient rule to simplify the expressions in Exercises. Assume that \(x>0.\) $$\sqrt{\frac{121}{9}}$$
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