Monomials & polynomials

Japanese school year: Junior high 2

What you learn

Learn how to add and subtract polynomials, multiply and divide monomials, and multiply or divide polynomials by numbers. Simplifying expressions by combining like terms forms the foundation for advanced algebraic calculations. Prior understanding of basic algebraic operations and the distributive property ensures smooth learning.

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Key points

This rule governs monomial multiplication. Multiply the numerical coefficients ( $a$ and $b$ ) together, and multiply the variable parts ( $x$ and $y$ ) together.

ax \times by = abxy

This formula calculates the division of monomials. Write the expression as a fraction with the divisor $by$ in the denominator, then simplify numbers and matching variables.

ax \div by = \frac{ax}{by} \quad (by \neq 0)

This rule expands a polynomial multiplied by a number $c$ . Using the distributive property, multiply $c$ by each individual term ( $ax$ and $by$ ) inside the parentheses.

c(ax + by) = cax + cby

This rule governs dividing a polynomial by a number $c$ . Each term in the polynomial ( $ax$ and $by$ ) must be individually divided by $c$ .

(ax + by) \div c = \frac{a}{c}x + \frac{b}{c}y \quad (c \neq 0)

Choose a set to practice.

Practice 1Coming soon