Question

`4x {}^(2) + 20x + 25`
using appropriate identity factories the following​

Answer 1

`\sf{\qquad\qquad\huge\underline{{\sf Answer}}}`

Let's Solve ~

`\qquad \sf  \dashrightarrow \: 4 {x}^(2) + 20x + 25`

`\qquad \sf  \dashrightarrow \: 4 {x}^(2) + 10x + 10x + 25`

`\qquad \sf  \dashrightarrow \: 2x(2x + 5) + 5(2x + 5)`

`\qquad \sf  \dashrightarrow \: (2x + 5) (2x + 5)`

`\qquad \sf  \dashrightarrow \: (2x + 5) {}^(2)`

or

`\sf{\qquad \sf  \dashrightarrow \: 4x² + 20x + 25 }`

`\sf{\qquad \sf  \dashrightarrow \: (2x)² + (2 \sdot 2x \sdot 5) + (5)²}`

[ it's similar to expression - a² + 2ab + b² that is equal to (a + b)² ]

so, let's use this identity here to factorise :

`\sf{\qquad \sf  \dashrightarrow \: (2x + 5)²}`

I hope it was helpful ~