Friday, November 6, 2015 Adding & Subtracting Linear Expressions

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Friday, November 6, 2015 Adding & Subtracting Linear Expressions + & ‒

term – the product of a coefficient and variables that may have exponents terms: 4x2y ½ab –3.7n 9 x like terms – terms with the exact same variable(s) to the same power(s) like terms: x and 3x 7y2 and –18y2 5a2bc4 and 26a2bc4 not like terms: x and 3 7y2 and –18y 5a2b and 26a2b2 linear expression – an algebraic expression in which the exponent of the variable is 1

0a) y + 5 linear b) 2a ‒ 3 c) 2a2 + 9 linear d) 10 ‒ y2 non-linear Determine if the following expressions are linear or non-linear. 0a) y + 5 b) 2a ‒ 3 c) 2a2 + 9 d) 10 ‒ y2 linear linear non-linear non-linear

To find the sum of linear expressions, distribute, then combine like terms. (2x – 2) + (5x + 5) 2x – 2 + 5x + 5 7x + 3 2) (‒6y + 9) + 3(y ‒ 4) ‒6y + 9 + 3y ‒ 12 ‒3y ‒ 3 Find common denominator of coefficients to add these terms.

Distributing Negatives A negative sign outside the parentheses is like multiplying by negative one→changes the sign of all terms in the parenthesis. ‒(3x + 2) = ‒1(3x + 2) = ‒3x ‒ 2

To find the difference of linear expressions, distribute, then combine like terms. BEWARE OF DISTRIBUTING NEGATIVES! 4) (4x – 1) ‒ (3x + 5) 4x – 1 – 3x – 5 x – 6 5) (‒8y + 7) – 2(y ‒ 4) ‒8y + 7 – 2y + 8 ‒10y + 15 Find common denominator of these terms to combine.