04 - Algebraic Techniques Path C Flashcards
(12 cards)
How do you simplify a fraction?
You must find any factors within two numbers, one being in the denominator, the other in the numerator, and divide it from the two numerals.
2x/5x = 2/5
How do you multiply fractions
You must cancel any common factors, also known as simplifying the fraction, and then multiply the enumerators and denominators separately
2x/5x × 2/5 = 4/25
How do you divide a fraction
You must multiply it by its reciprocal
2/5 ÷ 2/5 = 2/5 × 5/2 = 10/10 = 1
How do you factorise by grouping in pairs
In an expression using four terms, you must split the terms into two pairs and factorise them separately by determining the highest common factors of the pair, and multiplying the pair by the HCF
(3a + 6) + (ab + 2b) = 3(a +2) + b(a + 2) = (3 + b) (a + 2)
What is a perfect square
It is a binomial expression multiplied by itself.
(x + 3) (x + 3) = (x + 3)(2)
What is the difference of two squares?
It is when a pair of conjugates are multiplied together
(x + 3) (x - 3) = x(2) + 3x - 3x - 9 = x(2) - 9
What is a conjugate
It is when you change the sign (+, -, ×, ÷) in the middle of two terms.
How do you factorise by recognising the difference of two squares?
We must first take out the common factor of an expression, and then recognise the difference of two squares.
2x(2) - 18 = 2 (x(2) - 9) = 2 (x + 3) (x - 3)
How do you factorise monic quadratic trinomials?
We must find the two numbers that multiply to obtain the last number and add to obtain the middle number.
x(2) + 7x + 12 = (x + 3) (x + 4)
What is a trinomial?
It is an expression with 3 terms.
ax(2)
What’s a monic number
A number that is equal to 1
x
How do you factorise non-monic quadratic trinomials
You will have to find the product of the first and number number. From this product, we must find what else can be multiplied to obtain this product that are equal to the sum of the middle number. We keep the two outer number in place, but replace the middle number with the two numbers added to make the middle number. We can then factorise these binomial products.
3x(2) + x - 4 = -12
(3x(2) - 3x) (4x - 4) = 3x (x - 1) + 4 (x - 1) = (3x + 4) (x - 1)