Algebraic Expressions Flashcards
What is a term?
A number or letter on its own, or numbers or letters multiplied together.
What is an expression?
A set of terms combined by the + and - operations.
What is an equation?
Something that states two expressions are equal in value.
What is an identity?
A statement that is true no matter what values are chosen.
How do you combine added terms?
If the variable is the same, you just add the coefficients.
ax + bx = (a+b)x
How do you simplify multiplied terms?
Simply multiply the coefficient by the other coefficient and multiply the variable by the other variable.
ax * bx = ab(x^2)
ax * by = abxy
How do you expand a bracket?
You expand a bracket by multiplying everything on the inside of the bracket by everything on the outside.
a(bx + c) = abx + ac
How do you expand double brackets?
When expanding double brackets, everything in the first bracket must be multiplied by everything in the second bracket.
(ax + b)(cy + d) = acxy + bcy + adx + bd
How do you expand triple brackets?
When expanding triple brackets, you should firstly expand two of the brackets, and then multiply the remaining bracket by the expression.
(ax + b)(cy + d)(ez + f) = (acxy + bcy + adx + bd)(ez + f) =
acexyz + bceyz + adexz + bdez + acfxy + bcfy + adfx +bdf.
What is factorising?
Factorising is the opposite of expanding brackets. The answer will always include a set of brackets. To do it, you take out the highest common factor of all the terms.
How do you do basic factorising?
You look for common factors in the coefficients and then put these outside the brackets. You can then do this with variables too.
ax + ay = a(x + y)
ax + axy = ax(y + 1)
How can you demonstrate rules for even and odd numbers using algebra?
2p + 2n ≡ 2(p + n) E + E = E (2p + 1) + (2n + 1) ≡ 2(p + n + 1) O + O = E 2p + (2n + 1) ≡ 2(p + n) + 1 E + O = O (2p + 1) + 2n ≡ 2(p + n) + 1 O + E = O 2p x 2n ≡ 4pn ≡ 2(2pn) E x E = E (2p + 1)(2n + 1) ≡ 2(2pn + p + n) + 1 O x O = O 2p(2n + 1) ≡ 2(2pn + p) E x O = E (2p + 1)2n ≡ 2(2pn + p) O x E = E
What is a quadratic expression?
An expression in which the highest power is two.
How do you factorise an expression with no coefficient on the x^2?
x^2 + bx + c
You have to find two numbers that add to b and multiply to make c. Then, put them in the brackets added on to x.
(x + d)(x + e).
How do you factorise an expression with a coefficient on the x^2?
a(x^2) + bx +c
You multiply c by a. Then you look for factors of this new number and see if they can be added together to make b. If they can, you replace b with these factors. You then see if you can factorise this new expression.
