A term is a part of an expression that is connected to another term by a - or a - sign. For example, in the expression \( 4 x+6 y-9 z \), the terms are \( 4 x, 6 y \) and \( 9 z \). If there is no sign witten in front of a tom, it is alvays understood theat the sign is + . A (numerical) coefficlent is a factor by which the rest of a term is multipled. For example, the term \( 5 x y \) has a coefficient of 5 and the term \( -15 z \) has a coelficient of -15 . The degree of an expression is the highest exponent (or power) of any variable contained in the expression. For example, the expression \( 3 x+7 \) is a linear (or first degree) Expression, \( 9 x^{2}-4 x+1 \) is quadratic (or second degree) and \( 10 y^{3}+4 y^{2}-y+8 \) is cublic (or third degree). A linear equalion is therefore ono in which the largest value of the exponents is 1 . In an expression, terms that differ only in their coofficients are said to be like terms. For example, in the expression \( 15 x-5 y+32-4 x+6 x y+x^{2}+3 y \), the terms \( 15 x \) and \( -4 x \) are like terms. Also, th terms \( -5 y \) and \( +3 y \) are like terms. An equation is a statement that two expressions are equal. The two expressions are shown to be equal by m of an equals \( (=) \) sign. Example: Suppose that the two expressions \( 3 x+6 \) and \( 5 x-2 \) are equal. The resulting equation is:
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Did you know that ancient civilizations, like the Babylonians and Egyptians, were some of the first to use algebraic concepts? They had their own forms of equations and even solved quadratic equations, laying the groundwork for modern algebra. Their methods included geometric interpretations and computational techniques that paved the way for the mathematical tools we use today. They knew math was important, as it helped them in trade, astronomy, and even constructing monumental architecture! Now, when you’re solving equations, remember: a common mistake is forgetting to apply operations to both sides of the equation correctly! Always keep your operations balanced—what you do to one side, you must do to the other. And don’t forget to combine like terms before you start solving, as it makes the process simpler and clearer. Happy solving!
