Algebra and functions Flashcards
What does axᶜ+bxᶜ simplify to?
(a+b)xᶜ
What does aᵇaᶜ simplify to?
aᵇ⁺ᶜ
What does aᵇ/aᶜ simplify to?
aᵇ⁻ᶜ
What does (aᵇ)ᶜ simplify to?
aᵇᶜ
How can a⁻ᵇ be rewritten?
1/aᵇ
What does aᵇ/ᶜ simplify to?
ᶜ√aᵇ
How can (a₁+b₁+c₁+…)(a₂+b₂+c₂) be expanded?
Go through each term in the first bracket, and for each term, multiply it by each term in the second bracket, and the end result is the sum of these products
What does it mean for an expression to be fully factorised?
No terms inside the brackets have a common factor
What is a quadratic expression?
An expression of the form ax²+bx+c, where a, b and c are constants and a≠0
How can the quadratic expression ax²+bx+c be factorised into two brackets?
If a=1, then search for two numbers p and q such that p+q=b and pq=c, and then factorise into (x+p)(x+q). If a≠1, then search for four numbers m, n, p and q such that mn=a, mp+nq=b and pq=c, and then factorise into (mx+q)(nx+p)
What does a²-b² factorise to?
(a+b)(a-b)
What is n⁰ equal to, for n≠0?
1
What is √(ab) equal to?
√(a)*√(b)
What is √(a/b) equal to?
√(a)/√(b)
What is rationalisation?
The process of removing surds from the denominator of a fraction
