🟥 Algebraic Techniques Flashcards
(13 cards)
What is an algebraic fraction?
A fraction where the numerator, denominator, or both contain algebraic expressions.
What are the steps to simplify algebraic fractions?
- Factor if possible
- Cancel common factors
- Simplify
What are the steps to expand algebraic expressions?
Use distributive law:
a(b+c)=ab+ac
What is factorisation in algebra?
Writing an expression as a product of its factors, e.g.
x^2 +5x+6=(x+2)(x+3).
What techniques are used in simplifying and solving algebraic expressions?
Expanding
Collecting like terms
Using index laws
Factoring
Cancelling terms in fractions
What is the distributive property in algebra?
The distributive property allows you to multiply a number by terms in parentheses:
a(b+c)=ab+ac
How do you expand binomials using the distributive property?
Use the distributive property to expand:
(x+3)(x+2) = x^2 + 2x + 3x + 6 = x^2 + 5x + 6
What is the process of factoring quadratic expressions?
To factor a quadratic expression like
ax^2 + bx + c, find two numbers that multiply to give ac and add to give b. Then, split the middle term and factor by grouping.
Simplify the algebraic expression: 2x+3x
Combine like terms:
2x+3x= 5x
Expand the following expression:
(x+5)(x+2)
Use FOIL (First, Outer, Inner, Last):
xâ‹…x + xâ‹…2 + 5â‹…x + 5â‹…2 = x^2 + 2x + 5x + 10
Answer: 10x^2+7x+10
Factor the quadratic expression:
x^2 + 5x + 6
We need two numbers that add to 5 and multiply to 6 → 2 and 3.
x^2+5x+6=(x+2)(x+3)
Answer: (x+2)(x+3)
Simplify the algebraic fraction:
(3x^2 + 6x) / 3x
Factor the numerator:
= (3x(x+2))/3x
Cancel the common factor 3x
= x+2
Solve for x in the equation:
4(x+2)=3x+10
Step 1: Expand left side
4x+8=3x+10
Step 2: Move terms
4x−3x=10−8
x=2
