${ }_{10 C}$ 21 Assignment Booklet 3B ks) 8. Rahim and Kate are factoring $16 x^{2}+4 y^{2}$. Their solutions are as follows: Rahim \[ 16 x^{2}+4 y^{2}=4\left(4 x^{2}+y^{2}\right) \] Kate \[ \begin{aligned} 16 x^{2}+4 y^{2} & =4\left(4 x^{2}+y^{2}\right) \\ & =4(2 x+y)(2 x-y) \end{aligned} \] Who is correct? Explain your reasoning.

Step 1 ：First, let's check Rahim's solution by expanding it:

Step 2 ：\(16x^2 + 4y^2 = 4(4x^2 + y^2)\)

Step 3 ：\(16x^2 + 4y^2 = 16x^2 + 4y^2\)

Step 4 ：Rahim's solution matches the original expression.

Step 5 ：Next, let's check Kate's solution by expanding it:

Step 6 ：\(16x^2 + 4y^2 = 4(2x + y)(2x - y)\)

Step 7 ：\(16x^2 + 4y^2 = 16x^2 - 4y^2\)

Step 8 ：Kate's solution does not match the original expression.

Step 9 ：\(\boxed{\text{Rahim is correct, and Kate is incorrect.}}\)