Multiplication and Division of Binomials Multinomials -1st Quarter Grade 8 Matatag Revised K-12 Math

The lesson begins by explaining how to multiply binomials and other polynomials by a monomial using the distributive property, building on a previous lesson about multiplying monomials. It defines monomials as single-term polynomials and binomials as two-term polynomials, like 3x * (x + 4), and shows the step-by-step distribution and simplification process, including combining like terms.

The video demonstrates how to multiply a monomial by a trinomial, for example, -3x * (4x - 2y + 8), applying the distributive property to each term and carefully managing signs and exponents. It also covers multiplying a monomial by a multinomial, such as a²b³c * (2ab - 4c + 8c - 2), emphasizing the distribution to multiple terms and combining similar variables and coefficients while noting that variable bases do not add exponents.

This section explains how to divide binomials and multinomials by a monomial. The method involves dividing each term of the dividend by the monomial divisor. For example, (8x² + 4x³) / 4x. The numerical coefficients are divided, and for variables with the same base, their exponents are subtracted. The process is also applied to trinomials like (12a⁵ - 9a³ + 6a²) / -3a² and other more complex trinomials, highlighting careful handling of signs and exponents.

An activity is provided for viewers to practice the multiplication and division of polynomials involving monomials. This allows them to apply the learned concepts and check their understanding. Solutions are shown after a pause for independent work.

The video introduces three methods for multiplying binomials: distributive property, FOIL, and vertical form. The distributive property is explained first, showing how to multiply each term of the first binomial by each term of the second binomial, e.g., (x+8)(x+3), followed by combining similar terms to get the final answer.

The FOIL method (First, Outer, Inner, Last) is presented as an alternative for multiplying two binomials. Using the same example (x+8)(x+3), each step of FOIL is demonstrated, and how to combine the resulting terms, specifically the outer and inner products, to arrive at the final simplified polynomial.

The vertical method for multiplying binomials is explained, likening it to multi-digit multiplication. Binomials are stacked vertically, and terms are multiplied diagonally and then added, aligning similar terms before summing. An example (x+8)(x+3) is used, and a second example (x-5)(x+7) is walked through to illustrate the process of carrying over signs and combining terms.

An activity is given to practice multiplication of binomials using any of the three discussed methods. The presenter encourages viewers to choose their preferred method as all lead to the same correct answer. The video concludes by showing the correct answers to the activity and expressing gratitude to the viewers, encouraging them to subscribe for future math lessons.