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)
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.
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.