Question

How do you simplify the product `(2x - 5)(x + 4)` and write it in standard form?

Answer 1

`2x^2 + 3x - 20`

Explanation:

`(2x - 5 ) ( x + 4 )`

`2x xx x = 2x^2`

`2x xx 4 = 8x`

`-5 xx x = -5x`

`-5 xx 4 = -20`

`8x - 5x = 3x`

The answer is `2x^2 + 3x - 20`

Answer 2

`(2x-5)(x+4)=color(blue)(2x^2+3x-20)`

Explanation:

Expand:

`(2x-5)(x+4)`

When multiplying two binomials, use the FOIL method as shown below. Then combine like terms and simplify, which will result in the standard form for a quadratic equation, `ax^2+bx+c`.

`(2x-5)(x+4)`, where `ax=2x`, `b=-5`, `cx=x`, `d=4`.

Carry out the FOIL method for two multiplying binomials.

`(2x-5)(x+4)=2x*x+2x*4+(-5)*x+(-5*4)`

`(2x-5)(x+4)=2x^2+8x-5x-20`

Combine like terms.

`(2x-5)(x+4)=2x^2+8x-5x-20`

Simplify.

`(2x-5)(x+4)=color(blue)(2x^2+3x-20)` `lArr` standard form