Download Algebra 1 Formula Cheat Sheet and more Cheat Sheet Algebra in PDF only on Docsity! Formula Sheet 1 Factoring Formulas For any real numbers a and b, (a + b)2 = a2 + 2ab + b2 Square of a Sum (aโ b)2 = a2 โ 2ab + b2 Square of a Difference a2 โ b2 = (aโ b)(a + b) Difference of Squares a3 โ b3 = (aโ b)(a2 + ab + b2) Difference of Cubes a3 + b3 = (a + b)(a2 โ ab + b2) Sum of Cubes 2 Exponentiation Rules For any real numbers a and b, and any rational numbers p q and r s , ap/qar/s = ap/q+r/s Product Rule = a ps+qr qs ap/q ar/s = ap/qโr/s Quotient Rule = a psโqr qs (ap/q)r/s = apr/qs Power of a Power Rule (ab)p/q = ap/qbp/q Power of a Product Rule(a b )p/q = ap/q bp/q Power of a Quotient Rule a0 = 1 Zero Exponent aโp/q = 1 ap/q Negative Exponents 1 aโp/q = ap/q Negative Exponents Remember, there are different notations: q โ a = a1/q q โ ap = ap/q = (a1/q)p 1 3 Quadratic Formula Finally, the quadratic formula: if a, b and c are real numbers, then the quadratic polynomial equation ax2 + bx + c = 0 (3.1) has (either one or two) solutions x = โbยฑ โ b2 โ 4ac 2a (3.2) 4 Points and Lines Given two points in the plane, P = (x1, y1), Q = (x2, y2) you can obtain the following information: 1. The distance between them, d(P,Q) = โ (x2 โ x1)2 + (y2 โ y1)2. 2. The coordinates of the midpoint between them, M = ( x1 + x2 2 , y1 + y2 2 ) . 3. The slope of the line through them, m = y2 โ y1 x2 โ x1 = rise run . Lines can be represented in three different ways: Standard Form ax + by = c Slope-Intercept Form y = mx + b Point-Slope Form y โ y1 = m(xโ x1) where a, b, c are real numbers, m is the slope, b (different from the standard form b) is the y-intercept, and (x1, y1) is any fixed point on the line. 5 Circles A circle, sometimes denoted โ , is by definition the set of all points X := (x, y) a fixed distance r, called the radius, from another given point C = (h, k), called the center of the circle,โ def= {X | d(X, C) = r} (5.1) Using the distance formula and the square root property, d(X, C) = r โโ d(X,C)2 = r2, we see that this is precisely โ def= {(x, y) | (xโ h)2 + (y โ k)2 = r2} (5.2) which gives the familiar equation for a circle. 2
