Question

find (9x^ 2 -24xy+30xz-40yz+25z^ 2 +16y^ 2​

Answer 1

Answer:

$9 {x}^{2} - 24xy + 30xz - 40yz + 25 {z}^{2} + 16 {y}^{2} \\ \\We \: \: can \: \: factorise \: \: in \: \: three \: \: ways : \\ ⓵ \: \: 9 {x}^{2} - 24xy + 16 {y}^{2} \\ = {3}^{2} {x}^{2} - 24xy + {4}^{2} {y}^{2} \\ = {(3x)}^{2} - (2 \times 3x \times 4y) + {(4y)}^{2} \\ = \underline{ \underline{{(3x - 4y)}^{2}}} \\ \\ ⓶ \: \: 16 {y}^{2} - 40yz + 25 {z}^{2} \\ = {4}^{2} {y}^{2} - 40yz + {5}^{2} {z}^{2} \\ = {(4y)}^{2} - (2 \times 4y \times 5z) + {(5z)}^{2} \\ = \underline{ \underline{ {(4y - 5z)}^{2} }} \\ \\ ⓷ \: \: 9 {x}^{2} + 30xz + 25 {z}^{2} \\ = {3}^{2} {x}^{2} + 30xz + {5}^{2} {z}^{2} \\ = {(3x)}^{2} + (2 \times 3x \times 5z) + {(5z)}^{2} \\ = \underline{ \underline{ {(3x + 5z)}^{2} }}$