Help with Simplifying and Factoring!
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Help with Simplifying and Factoring!

[From: ] [author: ] [Date: 12-08-13] [Hit: ]
2) Multiply top & bottom by ( 2 √5 + 3 √2 )[Essentially you are using DoTS again.4, 5,9)Dividing by a fraction is the same as multiplying by the reciprocal of that fraction.......
I have a test coming up and these are some sample questions on the test.
If any one can give me step by step help on how to solve that would be wonderful.
I have not done this in about 4 years so the more thorough the explanation the better please. Thank you!

1) Factor completely 4(b+ 3a)² - 9 (b² + 3a)²


2) Rationalize the numerator , ( 2 √5 - 3 √2 ) / ( 2 √5 + 3 √2 )

3) Factor completely x ⁴ - y⁴ + 5x² -5y²

4) simplify (2x² y-² / 3x⁸ y⁷)⁹

5) simplify (( p^³/⁴ q^-²/³) / ( p^⁷/⁸ q^-³/⁴))²

6) simplify ∛xy ²z √x³yz²

7) find all the values of x, ( 2/ x-3) ² -3(2/ x-3)-4=0

8) Factor completely , 3x⁴y³ - 15x³y³ - 18x²y³

9) Simplify (a / 2b) / (1 / b²) - (2b / a ) / (1 / 2a)

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1) This is a difference of two squares (DoTS) use x² - y² = (x + y)(x - y)

2) Multiply top & bottom by ( 2 √5 + 3 √2 ) [Essentially you are using DoTS again.

3) Use DoTS

4, 5, 6) Use the index (power) laws

7) Multiply throughout by (x-3) ² this will give a quadratic

8) Take out 3x²y³ as a first factor

9) Dividing by a fraction is the same as multiplying by the reciprocal of that fraction.
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