# Expressions - Learning Outcomes 1 Expressions Learning Outcomes Perform addition, subtraction, multiplication, and division on polynomials and rational algebraic expressions. In particular, solve problems with brackets and surds. Apply the binomial theorem. 2 Perform Arithmetic on Polynomials Recall the key words used to describe polynomials: Constant a number separated by addition or subtraction.

Variable / unknown a letter of unknown value. Coefficient a number multiplied by one or more variables. 3 Perform Arithmetic on Polynomials Term any combination of numbers and variables separated by addition or subtraction. Expression any combination of terms. Perform Arithmetic on Polynomials Recall that expressions may not change value, so every statement must be equal to the last one. The expression toolbox contains anything to do with

simplifying and evaluating: Operating. Substituting. Commuting. Distributing. Factorising. Adding net zero. Multiply by net one. by Chromium Project BSD 4 5

Perform Arithmetic on Polynomials Operating performing arithmetic on constants, or terms with the same variables. e.g. e.g. Substituting replacing parts of an expression with something else with an equal value. e.g. e.g. Commuting swapping the order of numbers for certain operations: e.g. 6

Perform Arithmetic on Polynomials Distribution multiplication distributes over addition and powers distribute over multiplication. e.g. e.g. Factorisation breaking a number into its component factors and/or undistributing them. e.g. 7 Perform Arithmetic on Polynomials Adding net zero including adding a number in one place and subtracting it elsewhere. May help with

factorisation. e.g. Multiply by net one usually to help with factorisation or altering fractions. e.g. 8 Perform Arithmetic on Polynomials Simplify each of the following: 1. 2. 3. 4. 5.

6. 7. 8. 9 Perform Arithmetic on Polynomials Factorise the following as fully as possible: 1. 9. 2. 10.

3. 11. 4. 12. 5. 13. 6.

14. 7. 15. 8. 16. 10 Perform Arithmetic on Algebraic Fractions Recall that to add or subtract fractions, they must have the same denominator.

For algebraic fractions, the LCD is often the product of the denominators: e.g. LCD = 11 Perform Arithmetic on Algebraic Fractions Recall that to multiply fractions, simply multiply their numerators and multiply their denominators: e.g. To divide fractions, invert the divisor and make it a multiplication problem: e.g.

12 Perform Arithmetic on Algebraic Fractions Recall that fractions may be simplified if the numerator and denominator have a common factor: e.g. 13 Perform Arithmetic on Algebraic Fractions Simplify each of the following: 1. 7.

2. 8. 3. 9. 4. 10. 5.

11. 6. 12. 14 Solve Problems with Surds Surds are square roots of natural numbers. Since roots are indices , rules for indices apply: e.g. e.g.

15 Solve Problems with Surds Compound surds are a sum or difference of two numbers, at least one of which is a surd. e.g. , , The conjugate of a compound surd has the opposite sign. e.g. , , Evaluate: 1. 2. 3. 16

Solve Problems with Surds Simplify each of the following: 1. 7. 2. 8. 3. 9.

4. 10. 5. 11. 6. 12. 17 Apply the Binomial Theorem

The binomial theorem describes how to distribute binomials (expressions with two terms) with powers. e.g. 18 Apply the Binomial Theorem Use the binomial theorem to distribute the following: 1. 2. 3. 4. 5. 6.

What is the coefficient of in ?