# How do you simplify y = (x - 1)(5x + 2)?

Jun 20, 2016

$y = 5 {x}^{2} - 3 x - 2$

#### Explanation:

Multiply everything in one bracket by everything inside the other. WHATCH THE SIGNS!
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$\textcolor{b l u e}{\text{Method example using numbers}}$

Consider $6 \times 3 = 18$
But 6 can be 'split' (partitioned) into 4 + 2 so we have

$\left(4 + 2\right) \times 3 = 18$ The values have not changed, just the way they look.

Write as $3 \left(4 + 2\right)$

So this is 3 lots of $\left(4 + 2\right)$

$\to \text{ } \left(4 + 2\right) + \left(4 + 2\right) + \left(4 + 2\right)$

$= 4 + 4 + 4 \text{ } + 2 + 2 + 2$

$= 3 \times 4 \text{ "+" "3xx2" " =" " 12+6" "=" } 18$

So we have multiplied everything inside the bracket by 3

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Given:" "color(blue)((x-1)color(brown)((5x+2))

$\textcolor{b r o w n}{\textcolor{b l u e}{x} \left(5 x + 2\right) \textcolor{b l u e}{- 1} \left(5 x + 2\right)}$

$5 {x}^{2} + 2 x \text{ } - 5 x - 2$

$5 {x}^{2} - 3 x - 2$

$\textcolor{m a \ge n t a}{\text{Take it one step at a time }}$