Factorize completely 16y³+16y² +4y
16y³+16y² +4y
= 4y(4y^2 + 4y + 1)
= 4y(2y + 1)^2
To factorize the expression 16y³ + 16y² + 4y completely, you can first factor out the greatest common factor (GCF), which is 4y.
Step 1: Factor out the GCF:
4y(4y² + 4y + 1)
Next, observe that the expression inside the parentheses is a quadratic trinomial. To factorize it, you can either use the quadratic formula or try to factor it using the method of trial and error.
Step 2: Factorize the quadratic trinomial:
The quadratic trinomial 4y² + 4y + 1 cannot be factored any further, so we consider it as prime. Therefore, the fully factorized form of the expression is:
4y(4y² + 4y + 1)
To factorize the expression 16y³ + 16y² + 4y completely, we first look for the greatest common factor (GCF) of all the terms. In this case, the GCF is 4y since it can be divided evenly into each term.
So, we can start by factoring out the GCF, 4y, from each term:
4y(4y² + 4y + 1)
Next, we focus on factoring the quadratic expression within the parentheses, which is 4y² + 4y + 1.
To factor it, we need to find two numbers whose product is 1 and whose sum is 4. Since there are no such two numbers, we conclude that the quadratic expression is prime, and cannot be factored further.
Therefore, the completely factored form of the expression 16y³ + 16y² + 4y is:
4y(4y² + 4y + 1)