factor these problems

Question

12x²+11x-56

 

16x²-64x+64

 

4x²+20xy+25y²

 

18p⁴-84p²+98

 

4x²+4xy+y²-81

 

125p³-216q⁶

 

x⁴-81y²

 

x⁸-64y⁴

 

9a²-16b²

 

t³-27w³

 

64m³+n³

 

6x³-162

Answer 1

You want all of your homework done by someone else for free!

 

I'll select a couple and give you help, but you're going to have to learn from the examples in the book, in the lectures, and even from on line examples that you can find here and elsewhere.  To learn, YOU must DO.

 

16x²-64x+64 = 16(x²-4x+4) by taking out the GCF; then you should recognize the trinomial factor that remains as the perfect square, (x-2)².

 

x⁴-81y² = (x²-9y)(x²+9y) ... the DIFFERENCE of SQUARES .

 

The rest is up to you. Because you must try to apply the techniques that are being taught. Remember, once you think that you have the factoring done, YOU can check by multiplying out your solution--if you get exactly what you started with, you have succeeded.

Answer 2

When approaching factoring problems such as these, here are some useful tips:

 

1. Look for any common factors that each of the terms may share

 

16x² - 64x + 64 = 16(x² - 4x + 4) = 16(x - 2)(x - 2) = 16(x - 2)²

 

2. For the difference of two squares, we know that:

 

a² - b² = (a + b)(a - b)

 

x⁴ - 81y² = (x² + 9y)(x² - 9y)

 

3. For the difference of two cubes, we know that:

 

a³ - b³ = (a - b)(a² + ab + b²)

 

t³ - 27w³ = (t - 3w)(t² + 3wt + 9w²)

 

4. For the sum of two cubes, we know that:

 

a³ + b³ = (a + b)(a² - ab + b²)

 

64m³ + n³ = (4m + n)(16m² - 4mn + n²)

 

The examples in bold print should help you to factor the others