Can someone please tell me Why is (4x + 5) (2x - 1) + (x - 9) (2x - 1) not in factored form? What is the correct final factored form? What is this factoring method called?
To determine why (4x + 5)(2x - 1) + (x - 9)(2x - 1) is not in factored form, we need to simplify the expression.
First, let's identify the common factor in both terms: (2x - 1). By factoring out this common binomial, we can rewrite the expression as:
(2x - 1)[(4x + 5) + (x - 9)]
Now, we simplify the expression within the square brackets:
(2x - 1)(4x + 5 + x - 9)
Combine like terms:
(2x - 1)(5x - 4)
This is the simplified expression in factored form. To verify, we can distribute the binomial:
(2x - 1)(5x - 4) = 2x(5x) - 2x(4) - 1(5x) + 1(4) = 10x^2 - 8x - 5x + 4 = 10x^2 - 13x + 4
Therefore, the correct final factored form of the expression is (2x - 1)(5x - 4).
This factoring method, where we identify a common factor and factor it out, is called factoring by grouping.