Multiplication of Binomials using FOIL method and Vertical Form | Grade 8 | Q1 | Revised K-12 |

Summary

In this educational video, Teacher MJ explains how to multiply binomials using two methods: the FOIL method and the Vertical Form. The FOIL method is broken down into four steps—First, Outer, Inner, and Last—making it easy to follow. MJ also introduces the Vertical Form method, which involves multiplying each term in a vertical format. Through multiple examples, MJ emphasizes the importance of combining like terms for both methods. The video aims to make binomial multiplication easier to understand, providing students with helpful tips and clear explanations for mastering this algebraic concept.

Takeaways

• 😀 The FOIL method is a common and effective way to multiply binomials, where FOIL stands for First, Outer, Inner, and Last terms.
• 😀 In the FOIL method, 'First' refers to multiplying the first terms of the binomials, 'Outer' to the outer terms, 'Inner' to the inner terms, and 'Last' to the last terms.
• 😀 By following the FOIL method, binomials like (x + 2)(x + 5) can be expanded to x² + 7x + 10.
• 😀 A shortcut for applying the FOIL method is to directly calculate the products of the terms: x * x, x * 5, 2 * x, and 2 * 5.
• 😀 The vertical form is an alternative method for multiplying binomials, where you write the terms vertically and cross-multiply to obtain the result.
• 😀 In vertical form, you calculate each term separately and combine like terms to get the final expression.
• 😀 In the vertical method, for example, multiplying (x + 2)(x + 5) results in x² + 7x + 10, similar to the FOIL method.
• 😀 When multiplying binomials, it's essential to combine like terms if they have the same variable and exponent.
• 😀 The final answer of a binomial multiplication can often be simplified by adding or subtracting the like terms.
• 😀 It’s important to remember the sign rules when adding or subtracting terms. If both terms are negative, you copy the negative sign and add the numbers.
• 😀 The script emphasizes the value of practicing the FOIL method for easier and faster multiplication of binomials.

Q & A

What is the main topic of today's class?

The main topic of today's class is the multiplication of binomials using the FOIL method and vertical form.

What does each letter in the FOIL method represent?

In the FOIL method, F stands for the First terms, O for the Outer terms, I for the Inner terms, and L for the Last terms.

How do you apply the FOIL method to the binomials (x + 2) and (x + 5)?

To apply the FOIL method: First, multiply x by x to get x². Outer: multiply x by 5 to get 5x. Inner: multiply 2 by x to get 2x. Last: multiply 2 by 5 to get 10. Then combine like terms: 5x + 2x = 7x. The final result is x² + 7x + 10.

Why is it recommended to use the FOIL method rather than the step-by-step approach?

The FOIL method is faster and more efficient than writing out every individual multiplication step, making it easier to quickly arrive at the correct answer.

What does the 'vertical form' involve in multiplying binomials?

In vertical form, you multiply each term in one binomial by each term in the other, aligning the results vertically. Then, combine like terms at the bottom of the calculations to get the final result.

How does the vertical form work for multiplying (x + 2) and (x + 5)?

In vertical form: Multiply x by x to get x², x by 2 to get 2x, 5 by x to get 5x, and 5 by 2 to get 10. Afterward, combine like terms: 2x + 5x = 7x. The final result is x² + 7x + 10.

What is the key difference between the FOIL method and the vertical form?

The key difference is in how the terms are arranged. The FOIL method uses a specific order (First, Outer, Inner, Last), while the vertical form involves arranging the terms vertically and combining them afterward.

How do you handle negative signs when applying the FOIL method?

When handling negative signs, multiply according to the rules of signs. For example, multiplying a positive and negative number results in a negative product, while multiplying two negative numbers results in a positive product.

Can you explain how to handle terms like -6x and -4x in the FOIL method?

When adding terms like -6x and -4x, both have negative signs, so you simply add the absolute values (6 + 4 = 10) and keep the negative sign, resulting in -10x.

In the example (x - 6) and (x - 4), what is the final result after applying the FOIL method?

For the binomials (x - 6) and (x - 4), the steps are: First: x * x = x². Outer: x * -4 = -4x. Inner: -6 * x = -6x. Last: -6 * -4 = +24. Combine like terms: -4x + -6x = -10x. The final result is x² - 10x + 24.