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

Answer

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Answer

$Rahim is correct, and Kate is incorrect.$

Steps

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

Step 2 ： $16 x^{2} + 4 y^{2} = 4 (4 x^{2} + y^{2})$

Step 3 ： $16 x^{2} + 4 y^{2} = 16 x^{2} + 4 y^{2}$

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

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

Step 6 ： $16 x^{2} + 4 y^{2} = 4 (2 x + y) (2 x - y)$

Step 7 ： $16 x^{2} + 4 y^{2} = 16 x^{2} - 4 y^{2}$

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

Step 9 ： $Rahim is correct, and Kate is incorrect.$