Algebraic Expressions and Factorising: notes

Simplifying and Expanding

• Like terms: only terms with the same letters combine. 3x + 2x = 5x, but 3x + 2y stays as it is.
• Expanding: multiply every term inside the bracket. 3(x + 4) = 3x + 12. 2(x - 5) = 2x - 10.
• Two brackets: (x + 2)(x + 3) = x^2 + 5x + 6. Multiply each term by each term.
• Sign care: -(x - 3) = -x + 3. The minus changes both signs.

Factorising

• Common factor: take out the biggest one. 6x + 9 = 3(2x + 3).
• Difference of two squares: x^2 - 9 = (x - 3)(x + 3).
• Trinomial: x^2 + 5x + 6 = (x + 2)(x + 3). Find two numbers that multiply to 6 and add to 5.
• Grouping: ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y).

Formulae

• Substitution: put the numbers in, then follow BODMAS. If a = 2 and b = -3, then a^2 + b = 4 - 3 = 1.
• Change the subject: do the same to both sides. From v = u + at, a = (v - u) / t.
• Algebraic fractions: factorise, then cancel common factors. (x^2 - 4) / (x - 2) = x + 2.