Question

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

Answer 1

`y=x^2+7x+10`

Explanation:

The "standard form" for a quadratic is (in general)
`color(white)("XXX")y=ax^2+bx+c`
with constants `a, b, and c`

Answer 2

`y=x^2+7x+10`
Look at the method. It is using something called the 'Distributive' law

Explanation:

Given `y= (color(green)(x)color(red)(+)color(blue)(2))(x+5)`

`y=color(green)(x)(x+5) color(red)(+)color(blue)(2)(x+5)`

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Notice that the sign of the `color(blue)( 2)` follows it.
If the sign had been negative then we would have `color(red)(-)color(blue)(2)(x+5)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`y=(color(green)(x) xx x)+(color(green)(x) xx5)color(white)(....)+color(white)(....)(color(blue)(2) xx x)+(color(blue)(2)xx5)`

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

`y=x^2+7x+10`