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Chapter 5: Problem 38

Find each product. $$-b\left(a^{3}-a b+b^{3}\right)$$

Short Answer

Expert verified
The product is \(-ba^3 + ab^2 - b^4\).

Step by step solution

01

Identify the Variables

In this equation, variables 'a' and 'b' are involved in an algebraic expression.
02

Apply Distributive Property

Apply the distributive property which implies multiplying each term inside the parentheses by the term outside the parentheses. Therefore, -b multiplied by each term inside the parentheses \(a^3\), -ab and \(b^3\) gives \(-ba^3\), \(+ab^2\) and \(-b^4\).
03

Write Final Expression

Combine these products to get the final expression: \(-ba^3 + ab^2 - b^4\).

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Most popular questions from this chapter

In Exercises \(85-86,\) the variable \(n\) in each exponent represents a natural mumber. Divide the polynomial by the monomial. Then use polynomial multiplication to check the quotient. $$\frac{12 x^{15 n}-24 x^{12 n}+8 x^{3 n}}{4 x^{3 n}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$4^{-2}<4^{-3}$$

Perform the indicated operations. $$(x+5)(x-6)-(x+2)(x-9)$$

Explain how to multiply monomials. Give an example.

Perform the indicated computations. Express answers in scientific notation. $$\frac{\left(1.2 \times 10^{6}\right)\left(8.7 \times 10^{-2}\right)}{\left(2.9 \times 10^{6}\right)\left(3 \times 10^{-3}\right)}$$
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