Today's soundtrack is Sigur Ros: Kveikur, which I'm really digging.
I'm feeling much better today, and am now going to tackle part two of Chapter 21 of Basic Math & Pre-Algebra For Dummies. I fell asleep while working on it during the writing of yesterday's post, so I'm back to finish this one off.
Algebraic terms and the Big Four
To add like terms, add the coefficients and keep the variable the same. 2x + 4x = 6x. Unlike terms cannot be added.
To subtract like terms, subtract the coefficients and keep the variable the same. 4x - 3x = x. Unlike terms cannot be subtracted.
Both like and nonlike terms can be multiplied. Simply multiply the coefficients and then smush the variables together. 2x(4y) = 8xy; 2x(4x) = 8x².
To divide like or unlike variables, we make it into a fraction, then cancel out any factors from the coefficients that are "in both the numerator and the denominator" (p. 291), and cancel out any variables found in both numerator and denominator. We can only cancel out variables and coefficients if neither the numerator nor the denominator has any multi-term algebraic expressions.
Simplifying Algebraic Expressions
We simplify algebraic expressions to "make them easier to work with" (p. 292). There are several ways of simplifying expressions:
We can combine like terms: we rearrange an expression so that the like variables are next to each other, then calculate appropriately.
We can remove parentheses preceded by a plus sign, remembering that "when the first term inside the parantheses is negative [...], the minus sign replaces the plus sign. If a minus sign precedes the parentheses, then invert the sign of every term inside the parentheses, then remove the parentheses. If there is no symbol before the parentheses, simply multiply the terms inside the parentheses by the terms outside the parentheses.
If we are removing parentheses from two expressions without a sign between them, we need to "multiply every term inside the first set by every term inside the second" (p. 296). We do so with the FOIL method: We multiply the First, Outside, Inside, and Last terms (from first to last).
