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Chapter 5: Problem 54

Find each product. $$(x+5 y)(x-5 y)$$

Short Answer

Expert verified
The product of \( (x+5 y)(x-5 y) \) is \(x^2 -25y^2\)

Step by step solution

01

Apply the FOIL Method

Start by applying the FOIL method. Multiply the first terms in both binomials, then the outer terms, followed by the inner terms, and finally the last terms in each binomial: \(x \cdot x, x \cdot -5y, 5y \cdot x, 5y \cdot -5y\)
02

Simplify Each Term

Next, simplify each of the product terms we got from the FOIL method. \(x \cdot x = x^2\), \(x \cdot -5y = -5yx\), \(5y \cdot x = 5yx\), and \(5y \cdot -5y = -25y^2\)
03

Add All the Terms Together

Now, add all the terms together: \(x^2 -5yx + 5yx -25y^2\)
04

Reduce the Expression

Finally, we cancel the terms that nullify each other and the final expression becomes \(x^2 -25y^2\)

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Most popular questions from this chapter

In Exercises \(79-82,\) simplify each expression. Divide the sum of \((y+5)^{2}\) and \((y+5)(y-5)\) by \(2 y\)

Use a vertical format to find each product. $$\begin{array}{r}2 x^{3}+x^{2}+2 x+3 \\\\\quad x+4 \\\\\hline\end{array}$$

In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{8 x^{6} y^{3}-12 x^{8} y^{2}-4 x^{14} y^{6}}{-4 x^{6} y^{2}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$534.7=5.347 \times 10^{3}$$

Find the missing factor. $$(\quad ) \left(-\frac{1}{4} x y^{3}\right)=2 x^{5} y^{3}$$
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