Solve the following

Question

solve the following:

a) 3(2z+3)²-9(2z+3)-30

b)0.49k²-36m²

Answer 1

You can't really solve either of these since they're not equations (there's no equals sign), but you can fully factor them. Let's start with (a)...

 

 

3(2z+3)² - 9(2z+3) - 30

 

Let x = 2z + 3 and substitute that in to make a quadratic, then factor:

 

3x² - 9x - 30

3(x² - 3x - 10)

3(x - 5)(x + 2)

 

Now, substitute 2z + 3 = x back in and simplify:

 

3(2z + 3 - 5)(2z + 3 + 2)

3(2z - 2)(2z + 5)

 

This is fully factored.

 

 

For (b), you have...

 

0.49k² - 36m²

 

This expression is a difference of squares, which can be factored using this formula:

 

x² - y² = (x + y)(x - y)

 

√(0.49k²) = 0.7k and √(36m²) = 6m, so applying the formula to the original expression gives you:

 

(0.7k + 6m)(0.7k - 6m)

 

This is fully factored.