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What is the standard form of $y = (x + 2) (4 x + 1)$ $y= (x+2) (4x+1)$ ?

2 Answers

Dec 5, 2015

$y = 4 x^{2} + 9 x + 2$ $y=4x^2+9x+2$

Explanation:

The "standard form" for a quadratic equation is
$XXX y = a x^{2} + b x + c$ $color(white)("XXX")y=ax^2+bx+c$
with constants $a, b, c$ $a, b, c$

Given $y = (x + 2) (4 x + 1)$ $y=(x+2)(4x+1)$
we can convert this into standard form by simply multiplying the two factors on the right side:
$XXX (x + 2) (4 x + 1) = 4 x^{2} + 9 x + 2$ $color(white)("XXX")(x+2)(4x+1)=4x^2+9x+2$

Dec 5, 2015

$y = 4 x^{2} + 9 x + 2$ $y=4x^2+9x+2$

Explanation:

$y = (x + 2) (4 x + 1)$ $y=(x+2)(4x+1)$

Foil the two binomials.

![http://hubpages.com/education/Using-the-FOIL-Method-to-Expand-Products]( useruploads.socratic.org )

$a = x, b = 2, c = 4 x, d = 1$ $a=x, b=2, c=4x, d=1$

$y = (x \cdot 4 x) + (x \cdot 1) + (2 \cdot 4 x) + (2 \cdot 1)$ $y=(x*4x)+(x*1)+(2*4x)+(2*1)$

Simplify.

$y = 4 x^{2} + x + 8 x + 2$ $y=4x^2+x+8x+2$

Combine like terms.

$y = 4 x^{2} + 9 x + 2$ $y=4x^2+9x+2$

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