Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - 5x)

Verified step by step guidance

Identify the two binomials to be multiplied: $(7 - 3x)$ and $(-2 - 5x)$.

Apply the distributive property (also known as the FOIL method for binomials) to multiply each term in the first binomial by each term in the second binomial: multiply $7$ by $-2$, then $7$ by $-5x$, then $-3x$ by $-2$, and finally $-3x$ by $-5x$.

Write out each product explicitly: $7 \times (-2)$, $7 \times (-5x)$, $-3x \times (-2)$, and $-3x \times (-5x)$.

Simplify each product by performing the multiplication and combining constants and variables appropriately.

Combine all the simplified terms into a single expression and then combine like terms if any exist.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distributive Property

The distributive property allows you to multiply each term inside one parenthesis by each term inside the other. It is essential for expanding expressions like (7 - 3x)(-2 - 5x) by multiplying every term in the first binomial by every term in the second.

Combining Like Terms

After expanding the expression, you often get multiple terms with the same variable part. Combining like terms means adding or subtracting these terms to simplify the expression into a standard polynomial form.

Polynomial Multiplication

Multiplying two binomials results in a polynomial, typically of degree two. Understanding how to multiply polynomials helps in simplifying expressions and solving equations involving polynomial terms.

Recommended video:

03:42

Finding Zeros & Their Multiplicity

Related Practice

Textbook Question

Without solving the given quadratic equation, determine the number and type of solutions. $9 x^{2} = 2 - 3 x$

Textbook Question

In Exercises 59–94, solve each absolute value inequality. |3x - 8| > 7

Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 9 = 9(x + 1) - 4x

Textbook Question

Evaluate (x² + 19)/(2 - x) for x = 3i.

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3

views

Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x + 7 = 7(x + 1) - 3x