# What is the standard form of y= (2x^2+5)(x-2) + (x-4)^2?

Dec 25, 2017

$y = 2 {x}^{2} - 3 {x}^{2} - 3 x - 6$

#### Explanation:

1. FOIL (First, Outer, Inner, Last) Distribute the binomials.
$y = \left(2 {x}^{2} + 5\right) \left(x - 2\right) + {\left(x - 4\right)}^{2}$
$y = \left[\left(2 {x}^{2} \cdot x\right) + \left(2 {x}^{2} \cdot - 2\right) + \left(5 \cdot x\right) + \left(5 \cdot - 2\right) + \left(x - 4\right) \left(x - 4\right)\right]$
$y = \left(2 {x}^{3} - 4 {x}^{2} + 5 x - 10\right) + \left({x}^{2} - 8 x + 16\right)$

2. Note: A quick shortcut to FOILing squared binomials ${\left(x - 4\right)}^{2}$ is to square the first term, $x \to {x}^{2}$, multiplying the first time by the last term and then doubling it, $\left(x - 4\right) \to x \cdot - 4 \cdot 2 = - 8 x$, and then by squaring the last term, ${\left(- 4\right)}^{2} = + 16$
#(x-4)^2=x^2-8x+16)

$y = 2 {x}^{3} - 4 {x}^{2} + {x}^{2} + 5 x - 8 x - 10 + 16$
$y = 2 {x}^{2} - 3 {x}^{2} - 3 x - 6$