Question

What is the standard form of `f(x)=(x+5)^2`?

Answer 1

`x^2 + 10x + 25`

Explanation:

`(x + 5 )^2 = (x + 5 )(x + 5 )`

To distribute the brackets , each term in the 1st must multiply each term in the 2nd.

`color(blue) " (x + 5 ) " (x + 5 )`

`=color(blue) "x""(x + 5 )" +color(blue) "5" "(x + 5 )`

`= x^2 + 5x + 5x + 25 = x^2 + 10x + 25`

Answer 2

The "standard form" of a quadratic equation sets the expanded form of the expression to zero.

Explanation:

Expand the expression `(x+5)^2` : (x+5)(x+5) Complete the operations and set it equal to zero.

`x^2 + 10x +25 = 0`