Questions: Explain two ways in which (2 y+7)^2 and 4 y^2+28 y+49 are related. Choose the correct answer below. A. The product of 4 y^2+28 y+49 is (2 y+7)^2 and the factored form of 4 y^2+28 y+49 is (2 y+7)^2. B. The product of (2 y+7)^2 is 4 y^2+28 y+49 and the factored form of (2 y+7)^2 is 4 y^2+28 y+49. C. The product of 4 y^2+28 y+49 is (2 y+7)^2 and the factored form of (2 y+7)^2 is 4 y^2+28 y+49. D. The product of (2 y+7)^2 is 4 y^2+28 y+49 and the factored form of 4 y^2+28 y+49 is (2 y+7)^2.

Explain two ways in which (2 y+7)^2 and 4 y^2+28 y+49 are related.

Choose the correct answer below.
A. The product of 4 y^2+28 y+49 is (2 y+7)^2 and the factored form of 4 y^2+28 y+49 is (2 y+7)^2.
B. The product of (2 y+7)^2 is 4 y^2+28 y+49 and the factored form of (2 y+7)^2 is 4 y^2+28 y+49.
C. The product of 4 y^2+28 y+49 is (2 y+7)^2 and the factored form of (2 y+7)^2 is 4 y^2+28 y+49.
D. The product of (2 y+7)^2 is 4 y^2+28 y+49 and the factored form of 4 y^2+28 y+49 is (2 y+7)^2.

Transcript text: Explain two ways in which $(2 y+7)^{2}$ and $4 y^{2}+28 y+49$ are related. Choose the correct answer below. A. The product of $4 y^{2}+28 y+49$ is $(2 y+7)^{2}$ and the factored form of $4 y^{2}+28 y+49$ is $(2 y+7)^{2}$. B. The product of $(2 y+7)^{2}$ is $4 y^{2}+28 y+49$ and the factored form of $(2 y+7)^{2}$ is $4 y^{2}+28 y+49$. C. The product of $4 y^{2}+28 y+49$ is $(2 y+7)^{2}$ and the factored form of $(2 y+7)^{2}$ is $4 y^{2}+28 y+49$. D. The product of $(2 y+7)^{2}$ is $4 y^{2}+28 y+49$ and the factored form of $4 y^{2}+28 y+49$ is $(2 y+7)^{2}$.

Solution

Solution Steps

To determine the relationship between $(2y+7)^2$ and $4y^2+28y+49$, we need to expand $(2y+7)^2$ and compare it to the polynomial $4y^2+28y+49$. If they are equal, then $(2y+7)^2$ is the factored form of $4y^2+28y+49$, and vice versa.

Step 1: Expand $(2y + 7)^2$

To find the relationship between $(2y + 7)^2$ and $4y^2 + 28y + 49$, we first expand the expression: \[ (2y + 7)^2 = 4y^2 + 28y + 49 \]

Step 2: Compare the Expanded Expression

The expanded form $4y^2 + 28y + 49$ is identical to the polynomial given in the question. This shows that: \[ (2y + 7)^2 = 4y^2 + 28y + 49 \]

Step 3: Identify the Factored Form

Since we have established that $(2y + 7)^2$ expands to $4y^2 + 28y + 49$, we can conclude that the factored form of $4y^2 + 28y + 49$ is $(2y + 7)^2$.