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Chapter 0: Problem 26

Find each product. $$(2 x-5)(7 x+2)$$

Short Answer

Expert verified
The product of the two binomials \((2 x-5)(7 x+2)\) is \(14x^2 - 31x - 10\)

Step by step solution

01

Multiply the First Terms

Multiply the 'first' terms in each binomial. This means you multiply the 2x in the first binomial by the 7x in the second binomial. This results in a product of \(14x^2\).
02

Multiply the Outer Terms

Next, multiply the 'outer' terms. Here, the outer terms are 2x from the first binomial and 2 from the second binomial, which gives us a product of \(4x\).
03

Multiply the Inner Terms

The 'inner' terms are -5 from the first binomial and 7x from the second binomial. The product of these terms is \(-35x\).
04

Multiply the Last Terms

The last terms are -5 from the first binomial and 2 from the second binomial. Their product is \(-10\).
05

Combine Like Terms

Now add up the four terms. \(14x^2 + 4x - 35x -10\). We can combine the middle two terms to simplify this to \(14x^2 - 31x - 10\).

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Most popular questions from this chapter

Explain how to factor \(3 x^{2}+10 x+8\)

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(49 x^{-2} y^{4}\right)^{-\frac{1}{2}}\left(x y^{\frac{1}{2}}\right) $$

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Describe what it means to raise a number to a power. In your description, include a discussion of the difference between \(-5^{2}\) and \((-5)^{2}\)
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