Here are two easy methods to expand and simplify expressions with common mistakes and tips.
NORMAL METHOD
2 ( 5x - 2 ) + 8 ( - 4x + 6 )
First step - First you are going to use the first number (2) to multiply the terms in the first bracket.
( 5x - 2 )
Second step - Secondly you are going to use the second number (8) to multiply the terms in the second bracket. ( - 4x + 6 )
Third step - Write down the results you got after expanding the brackets. ( 10x - 4 - 32x + 48 )
Fourth step - Thirdly you are going to combine/group the like terms together. ( 10x - 32x - 4 + 48)
Last step - Lastly you are now going to rewrite the result in the order they've been grouped.
( -22x + 44 )
Written Example :
2 * 5x + 2 * - 2 + 8 * - 4x + 8 * 6
10x - 4 - 32x + 48
10x - 32x - 4 + 48
-22x + 44
These are some common mistakes students often make when expanding and simplifying:
1. When combining they don't write back the sign that is in-front of the term.
2. They didn't expand properly.
3. They only expand and didn't simplify.
4. They don't follow all steps to show what they are doing.
How to solve these mistakes?
1. Always pay attention to your negative and positive signs.
2. Its best to follow all steps so you won't get confused during the process.
3. Follow the instruction and do both expanding and simplifying.
4. Double check your answers to make sure you didn't make a mistake.
FOIL METHOD
(3x + 2)(8x - 4)
First step: Firstly you will use the first term in the first bracket to multiply all the terms in the second bracket.
3x * ( 8x - 4)
Second step: Secondly you will now use the second term in the first bracket to multiply all the terms in the second bracket. 2 * ( 8x - 4)
Third step: Thirdly you will write any term with an exponent first and then group any other terms like terms.
24x^2 - 12x + 16x - 8
Fourth steps: Solve for the final result. 24x^2 + 4 - 8
Written example:
3x * 8x + 3x * -4 + 2 * 8x + 2 * -4
24x^2 - 12x + 16x - 8
24x^2 + 4 - 8
These are some common mistakes students often make when expanding and simplifying:
1. Multiply the terms in the same bracket.
2. Multiply the wrong terms.
3. Forget to write the terms with the exponents first.
How to solve these mistakes?
1. Always pay attention to the terms that should be multiplied.
2. Always follow the "FOIL" method to never go wrong.
3. When re-writing and grouping always pay keen attention.
Here are two worksheets for you to try using both methods :
Have fun !!!
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