Manipulation of algebraic expressions Flashcards
How does the distributive law work?
You multiply the term outside a bracket with each term inside the bracket
How do you expand the product of two binomials?
Each term in the first bracket is multiplied by each term in the second bracket.
What is the first thing to check when solving factorisation problems?
Check if there is a HCF and take it out if its there.
How do you factorise a difference of two squares?
(square root of first term + square root of second term)(square root of first term - square root of second term)
How do you factorise a trinomial of the form ax^2 + bx + c where a = 1?
(x +- ___)(x +- ___)
Look for factors of c such that their sum = b and their product = c.
How do you factorise a trinomial of the form ax^2 + bx + c where a is not equal to 1?
Using the cross method.
What are the steps of the cross method?
Step 1: List all factors of a on one side of the cross.
Step 2: List all factors of c on the other side of the cross.
Step 3: Multiply diagonally across the lines and obtain two answers
Step 4: Add the two numbers, and they should equal to b
Step 5: First bracket is the two numbers at the top and second bracket is the numbers at the bottom.
How do you factorise an expression with 4 terms?
Group in pairs.
Step 1: Look for HCF in each pair and factorise each pair
Step 2: Take out the common bracket and write the second bracket.
What is the procedure for factorizing the sum/difference of two cubes?
Step 1: Write out two brackets
Step 2: For the first bracket, cube root each term and keep the same sign
Step 3: For the second bracket, square the first term, change the sign and multiply both terms together and lastly, square the last term.
N.B The sign of the last term is always positive.
What is the condition that needs to be satisfied before adding or subtracting fractions?
Fractions can only be added or subtracted if they have the same denominator.
