Factor this expression completely. 35x−40
To factor the expression 35x - 40 completely, we can first factor out the greatest common factor (GCF) of the two terms, which is 5:
35x - 40 = 5(7x - 8).
The expression 7x - 8 cannot be factored further, so the factored form of the expression 35x - 40 is 5(7x - 8).
Factor the expression completely. 45x−18y+36
To factor the expression completely, we can first look for any common factors among the coefficients of the terms, which, in this case, is 9:
45x - 18y + 36 = 9(5x - 2y + 4).
The expression 5x - 2y + 4 cannot be factored any further, so the completely factored form of the expression 45x - 18y + 36 is 9(5x - 2y + 4).
To factor the expression 35x - 40 completely, we need to look for common factors in both terms.
First, we can factor out the greatest common factor, 5, from both terms:
35x - 40
= 5(7x - 8)
Now, let's check the expression (7x - 8) to see if it is factorable further.
We notice that it is a difference of squares.
We can write (7x - 8) as (√7x - √8)(√7x + √8).
However, we can simplify further by finding the square roots of 7x and 8.
The square root of 7x can be written as √(7x) or √7 * √x.
And the square root of 8 can be written as √(8) or 2√2.
Therefore, the fully factored expression is:
5(√7 * √x - 2√2)(√7 * √x + 2√2)
To factor the expression 35x - 40 completely, we need to find the greatest common factor (GCF) of the terms in the expression. In this case, both terms share a common factor of 5. So, we can start by factoring out 5:
35x - 40 = 5(7x - 8)
Now, the expression is partially factored. To see if we can further factor, we can check if the binomial (7x - 8) can be factored.
In this case, the binomial (7x - 8) cannot be factored any further since there are no common factors between 7 and 8.
Therefore, the completely factored form of the expression 35x - 40 is 5(7x - 8).