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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 5: Q.228. (page 537)

Multiply each pair of conjugates using the product of the conjugates pattern.
$(5 k + 6) (5 k - 6)$

Short Answer

Expert verified

The solution is $25 k^{2} - 36$ .

Step by step solution

01

Step 1. Given information.

The given expression is $(5 k + 6) (5 k - 6)$ .

02

Step 2. Simplify the expression by using the difference of squares a+ba-b=a2-b2.

Solve it as follows:

$(5 k + 6) (5 k - 6) = {(5 k)}^{2} - {(6)}^{2} \Rightarrow 25 k^{2} - 36$

03

Step 3. Binomial squares expression.

Hence, the binomial squares pattern are $25 k^{2} - 36$ .

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Most popular questions from this chapter

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial $(a) - 5 (b) 8 y^{3} - 7 y^{2} - y - 3 (c) - 3 x^{2} y - 5 x y + 9 x y^{3} (d) 81 m^{2} - 4 n^{2} (e) - 3 x^{6} y^{3} z$

In the following exercises, find the product of ${(9 p + 8 q)}^{2}$ .

Find the product of the below expression.

$(2 x + y) (x - 2 y)$

Multiply : (a) (-6b⁴)(-9b⁵)

(b) $(\frac{2}{3} r^{5} s) (12 r^{6} s^{7})$

In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method

$(y + 9) (y + 3)$

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