Math, asked by supritis, 1 month ago

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

Answers

Answered by harshitha202034
0

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} }}

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