# Which among the following is not a factor of 4y(y+3)? (A) y^2+3y (B) 4y^2 (C) 4(y+3) None of these

## Question

Which among the following is not a factor of $4y(y+3)$? (A) $y^2+3y$ (B) $4y^2$ (C) $4(y+3)$ None of these

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## Answer

The correct option is **(B)**
$$4y^2$$

Let's express $4y(y+3)$ in a detailed factorized form: $$ 4y(y + 3) = 4 \times y \times (y + 3) = 4y \times (y + 3) = 4(y + 3) \times y = 4 \times y(y + 3) $$

Now, analyzing the factors:

- $y(y + 3)$: Clearly, $y(y + 3)$ is a factor of $4y(y + 3)$.
- $4(y + 3)$: This can be directly seen as $4(y + 3)$ is a multiplication component within $4y(y + 3)$.
- $4y$: It is also evident as $4y$ multiplies $(y + 3)$ in the expression $4y(y + 3)$.

To break down $4y(y + 3)$, we get: $$ 4y(y + 3) = 4y^2 + 12y $$

So, while $4y^2$ appears as a term in the expansion, it is **not** an individual factor of the whole expression $4y(y + 3)$.

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