how do i factorise:
a)5a^2b+ab^2
b)9k^2-1
c)2y^2-5y+2
a) ab(5a+b)
b) (3k+1)(3k-1)
c) (2y-1)(y-2)
To factorize the given expressions, we need to look for common factors or apply appropriate factorization techniques. Let's break down each expression separately:
a) 5a^2b + ab^2
To factorize this expression, we can find the common factors in both terms. In this case, the common factor is ab.
So, we can rewrite the expression as:
ab(5a + b)
Therefore, the factored form of 5a^2b + ab^2 is ab(5a + b).
b) 9k^2 - 1
This expression resembles a difference of squares, which can be factored using the following identity:
a^2 - b^2 = (a + b)(a - b)
In this case, a = 3k and b = 1. So, we can rewrite the expression as:
(3k)^2 - 1^2
Using the difference of squares formula, we have:
(3k + 1)(3k - 1)
Therefore, the factored form of 9k^2 - 1 is (3k + 1)(3k - 1).
c) 2y^2 - 5y + 2
To factorize this quadratic expression, we need to break down the middle term (-5y) into two terms whose coefficients multiply to give the product of the coefficients of the first and third terms.
The coefficient of y^2 is 2, the coefficient of the constant term is 2, and the coefficient of y is -5.
We need to find two numbers whose product is 2 * 2 = 4 and whose sum is -5.
In this case, the numbers are -4 and -1 because (-4) * (-1) = 4, and (-4) + (-1) = -5.
Now, we can rewrite the expression as:
2y^2 - 4y - y + 2
Taking common factors, we get:
2y(y - 2) - 1(y - 2)
Now, notice that both terms have a common factor of (y - 2). Hence, we can factor it out:
(y - 2)(2y - 1)
Therefore, the factored form of 2y^2 - 5y + 2 is (y - 2)(2y - 1).
Remember, factorizing expressions may involve identifying common factors, applying factorization identities/formulas, and rearranging terms to simplify the expression.