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Chapter 5: Problem 59

Find each product. Use the FOIL method. $$ (3 t-4 s)(t+3 s) $$

Short Answer

Expert verified
\[3t^2 + 5ts - 12s^2\]

Step by step solution

01

Identify the terms

Identify each term in the binomials: First binomial: First term (F) = 3t Second term (L=-4s). Second binomial: First term (F) = t Second term (L= 3s).
02

First terms multiplication

Multiply the first terms from each binomial: o Left first term: 3t o Right first term: t o Multiply: \[(3t)(t) = 3t^2\]
03

Outside terms multiplication.

Multiply the outer terms: o Left first term: 3t o Right second term: 3s o Multiply: t o Multiply: \[(3t)(3s) = 9ts\]
04

Inside terms multiplication

Multiply the inner terms: o Left second term: -4s o Right first term: t o Multiply: \[(-4s)(t) = -4ts\]
05

Last terms multiplication

Multiply the last terms of each binomial: o Left second term: -4s o Right second term: 3s o Multiply: \[(-4s)(3s) = -12s^2\]
06

Combine all products

Combine all the products from steps 3 to 5. The equation becomes \[3t^2 + 9ts - 4ts - 12s^2\]
07

Simplify the expression.

Combine like terms: o The 9ts & -4ts are like terms, combine them: Left overs: o Combine: 9ts - 4ts = 5ts. Final equation: \[3t^2 + 5ts - 12s^2\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Binomials Multiplication
Binomials multiplication is a crucial concept in algebra.
A binomial is an algebraic expression with exactly two terms, like \(3t - 4s\) and \(t + 3s\).

When we multiply binomials, we use a specific method called the

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Most popular questions from this chapter

Evaluate each expression for \(x=3\) $$ 3 x^{2}-3 x+4 $$

Evaluate. $$ 6504 \div 100 $$

To understand how the special product \((a+b)^{2}=a^{2}+2 a b+b^{2}\) can be applied to a purely numerical problem. The number 35 can be written as \(30+5 .\) Therefore, \(35^{2}=(30+5)^{2} .\) Use the special product for squaring a binomial with \(a=30\) and \(b=5\) to write an expression for \((30+5)^{2} .\) Do not simplify at this time.

Simplify by writing each expression with positive exponents. Assume that all variables represent nonzero real numbers. See Example \(5 .\) $$ \frac{\left(m^{8} n^{-4}\right)^{2}}{m^{-2} n^{5}} $$

Find each product. In Exercises \(81-84,89,\) and \(90,\) apply the meaning of exponents. $$ 3 p^{3}\left(2 p^{2}+5 p\right)\left(p^{3}+2 p+1\right) $$
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