Actions with binomials — lesson. Mathematics CBSE, Class 7.

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When multiplying or dividing a monomial by a number, we multiply or divide only its coefficient.

Example:

\begin{array}{l} 6 x \cdot 5 = 30 x; \\ - 0, 5 zy \cdot 2 = - zy; \\ 4 x^{2} : 2 = 2 x^{2} \end{array}

A binomial is an algebraic sum of monomials.

Example:

\begin{array}{l} 3 x + 2 y; \\ 4 xy - 6 y^{2} \end{array}

When multiplying or dividing a binomial by a number, each term is multiplied or divided.

Example:

\begin{array}{l} 2 \cdot (2 x + 4 y) = 4 x + 8 y; \\ (- x + y^{2}) \cdot (- 3) = 3 x - 3 y^{2}; \\ (6 x - 4 y + c) : 2 = \\ = 3 x - 2 y + \frac{c}{2} = \\ = 3 x - 2 y + 0,5 c . \end{array}

Actions with the like terms:

\begin{array}{l} 2 x + 5 - x + 8 y - 3 y = \\ = \underline{2 x} + 5 - \underline{x} + \underline{\underline{8 y}} - \underline{\underline{3 y}} = \\ = x + 5 y + 5 \end{array}

Important!

Terms of binomials are often written in brackets. In this case, attention should be paid to the sign in front of the brackets:

\begin{array}{l} + (a + b) = a + b \\ - (a + b) = - a - b \end{array}

\begin{array}{l} c - (2 a - b) + 2 (x - y) = \\ = c - 2 a + b + 2 x - 2 y \end{array}

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2. Actions with binomials