Expanding Brackets

Expanding Brackets

H1 Expanding Single Brackets

• A term outside of the bracket must be multiplied by each term inside of the bracket
• Apply the distributive law: a(b + c) = ab + ac
• For example, expand 3(x + 2), 3 multiplied by x is 3x, and 3 multiplied by 2 is 6, so it expands to 3x + 6

H1 Expanding Double Brackets

• When expanding double brackets, remember the method: first, outside, inside, last (FOIL)
• First apply the FOIL method: expand (a + x)(b + y) to get ab + ay + bx + xy
• For example, expand (x + 2)(x - 3), first: xx = x^2, outside: x(-3) = -3x, inside: 2x= 2x, last: 2(-3)= -6. Final Result: x^2 - 3x + 2x - 6 = x^2 - x - 6

H1 Special Cases in Expanding Brackets

• Recognize perfect squares: Implement the rule (x + a)^2 = x^2 + 2ax + a^2
• For example, (x + 3)^2 = x^2 + 6x + 9
• Pay special attention to difference of two squares: (a + b)(a - b) = a^2 - b^2
• For example, with (x + 6)(x - 6), the answer will be x^2 - 36