i'm having troubles with some sums
how would you factorize completely
9a(squared) - b(squared)?
or an expression like
27x(squared) - 1/3y(squared)
its difficult. have many more.
9a^2 - b^2
= (3a)^2- (b)^2
= (3a+b)(3a-b)
i couldn't understand the second one though. Hope it helps!!! :-)
whenever you have the difference of two squares
the factors are the sum and the difference of the two that are squared.
a^2-b^2 ( a + b )( a - b )
27x(squared) - 1/3y(squared)
first take (1/3) out
(1/3) (3^4 x^2 - y^2)
(1/3)(3^2 + y)(3^2 - y)
(1/3)(9+y)(9-y)
1/3) (3^4 x^2 - y^2)
(1/3)(3^2 x + y)(3^2 - y)
(1/3)(9x+y)(9x-y)
To factorize completely, you need to identify common factors and then apply special factoring formulas if applicable. Let's factorize the expressions you provided step by step.
1. Factorizing 9a² - b²:
This expression is a difference of squares. To factorize a² - b², you can use the formula (a + b)(a - b).
Therefore, 9a² - b² = (3a + b)(3a - b).
2. Factorizing 27x² - 1/3y²:
In this expression, we first notice that both terms have a factor of 3. We can factor it out:
27x² - 1/3y² = 3(9x² - 1/9y²).
Now, inside the parentheses, we have another difference of squares:
9x² - 1/9y² = (3x + 1/3y)(3x - 1/3y).
Putting it all together:
27x² - 1/3y² = 3(3x + 1/3y)(3x - 1/3y).
Remember to simplify the resulting expressions wherever possible.
If you have more expressions you would like help with, please provide them, and I will be happy to assist you with factorizing them.