UNLOCKSFactor a simple quadratic with integer coefficients by finding factor data whose product and sum reproduce the constant and linear coefficientsRecognise and factor a difference of two squares, a perfect-square trinomial, and a sum or difference of two cubes, with the correct sign patternForm the coefficient and exponent data of a binomial power, including alternating signs for subtraction, and write the terms in descending powers of the first algebraic factorMultiply and expand exact surd expressions using the distributive law, simplify radical products, collect like terms and use conjugates where they occurRewrite a rule in canonical a·f(n(x−h))+k form and connect a, n, h and k with vertical dilation or reflection, horizontal dilation, phase shift and vertical translation CH 10Form and simplify the secant-gradient difference quotient (f(x+h)−f(x))/h for a polynomial or simple power function, expanding f(x+h) exactly and cancelling the common factor of h before any limit is taken CH 12Simplify a polynomial to an explicit sum of powers where necessary and produce its complete derivative in descending-power form, including zero coefficients where the response table labels them CH 12Identify an objective and constraint, eliminate extra variables exactly and state a one-variable objective with its feasible domain CH 13Expand, divide by a common monomial, simplify radicals or rewrite reciprocal powers until the integrand is an explicit sum of admissible powers before applying the rule CH 14