\( \begin{array}{lll}\text { (a) } x^{2}+\ldots+16 & \text { (b) } 4 a^{2}+\ldots+y^{2} & \text { (c) } p^{2}-\ldots .+36 \\ \text { (d) } 9 a^{2}-\ldots+16 b^{2} & \text { (e) } 25 p^{2}-\ldots \ldots+49 q^{2} & \text { (f) } p^{2}+\ldots \ldots+\frac{4}{p^{2}} \\ \text { (g) } 225 x^{2}-\ldots+64 y^{2} & \text { (h) } 1+\ldots \ldots+36 y^{2} & \text { (i) } p^{2}-\ldots \ldots+\frac{1}{p^{2}}\end{array} \)

It looks like you have a series of expressions that are likely meant to be completed as perfect squares or to be factored. Let's analyze each expression and fill in the blanks accordingly. ### (a) \( x^{2} + \ldots + 16 \) This expression can be completed as: \[ x^{2} + 0x + 16 = (x + 0)^2 + 16 \] However, if we want to express it as a perfect square, we can write: \[ x^{2} + 0x + 16 = (x - 4)^2 + 0 \] So, the completed expression is: \[ x^{2} - 8x + 16 = (x - 4)^2 \] ### (b) \( 4a^{2} + \ldots + y^{2} \) This can be expressed as: \[ 4a^{2} + 0a + y^{2} = (2a + 0)^2 + y^{2} \] To express it as a perfect square: \[ 4a^{2} + 0a + y^{2} = (2a)^2 + (y)^2 \] ### (c) \( p^{2} - \ldots + 36 \) This can be completed as: \[ p^{2} + 0p + 36 = (p + 0)^2 + 36 \] To express it as a perfect square: \[ p^{2} - 0p + 36 = (p - 6)^2 \] ### (d) \( 9a^{2} - \ldots + 16b^{2} \) This can be expressed as: \[ 9a^{2} + 0a + 16b^{2} = (3a)^2 + (4b)^2 \] ### (e) \( 25p^{2} - \ldots + 49q^{2} \) This can be expressed as: \[ 25p^{2} + 0p + 49q^{2} = (5p)^2 + (7q)^2 \] ### (f) \( p^{2} + \ldots + \frac{4}{p^{2}} \) This can be expressed as: \[ p^{2} + 0p + \frac{4}{p^{2}} = (p + \frac{2}{p})^2 \] ### (g) \( 225x^{2} - \ldots + 64y^{2} \) This can be expressed as: \[ 225x^{2} + 0x + 64y^{2} = (15x)^2 + (8y)^2 \] ### (h) \( 1 + \ldots + 36y^{2} \) This can be expressed as: \[ 1 + 0 + 36y^{2} = (1)^2 + (6y)^2 \] ### (i) \( p^{2} - \ldots + \frac{1}{p^{2}} \) This can be expressed as: \[ p^{2} + 0p + \frac{1}{p^{2}} = (p + \frac{1}{p})^2 \] In summary, the completed expressions are: - (a) \( x^{2} - 8x + 16 \) - (b) \( 4a^{2} + 0a + y^{2} \) - (c) \( p^{2} - 0p + 36 \) - (d) \( 9a^{2} + 0a + 16b^{2} \) - (e) \( 25p^{2} + 0p + 49q^{2} \) - (f) \( p^{2} + 0p + \frac{4}{p^{2}} \) - (g) \( 225x^{2} + 0x + 64y^{2} \) - (h) \( 1 + 0 + 36y^{2} \) - (i) \( p^{2} + 0p + \frac{1}{p^{2}} \) If you have specific values or further instructions for these expressions, please let me know!