1b.+Algebra+-+Misconceptions

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//This page assumes a basic grasp of fundamental algebraic concepts - it does not discuss misconceptions and common errors for introductory algebra (early high school).//

3. Expanding Perfect Squares and Difference of Squares Products
Every time someone does this: math (a + b)^2 = a^2 + b^2 \quad \text{ Wrong!} math you are stealing from the binomial gnomes: When you do this, you are "clipping my coin ", you are stealing 2 x ab. Isaac Newton himself as Master of the Mint in 1699 punished coin clippers with great severity. Don't do it! Life is hard enough for these little fellows without you stealing from them.

11. Factorising Sum and Difference of Cubes
math a^3 + b^3 = (a + b) ( a^2 + ab + b^2) \quad \text{Wrong!} math It should of course be: math a^3 + b^3 = (a + b) ( a^2 - ab + b^2) \quad \text{Correct} math math 125p^3 - 216q^3 = (5p - 6q)(25p^2 + 30pq + 36q) \quad \text{Wrong!} math instead of math 125p^3 - 216q^3 = (5p - 6q)(25p^2 + 30pq + 36q^2) \quad \text{Correct} math
 * It's way too easy to mix up the addition and substraction signs. Most likely because it feels odd to put in the minus sign in an expression that has just positive signs.
 * It's easy to forget to square the last term - especially if there are many numbers to keep in your head. eg: