Simplify the expression (-2y+5)(y+3)

Mathematics

1 answer:

dsp733 years ago

6 0

Answer:

$=-2y^2-y+15$

Step-by-step explanation:

$\left(-2y+5\right)\left(y+3\right)\\\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\a=-2y,\:b=5,\:c=y,\:d=3\\=\left(-2y\right)y+\left(-2y\right)\cdot \:3+5y+5\cdot \:3\\Apply\:minus-plus\:rules\\+\left(-a\right)=-a\\=-2yy-2\cdot \:3y+5y+5\cdot \:3\\\mathrm{Simplify}\:-2yy-2\cdot \:3y+5y+5\cdot \:3:\quad -2y^2-y+15\\-2yy-2\cdot \:3y+5y+5\cdot \:3$

$2yy=2y^2\\2yy\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\yy=\:y^{1+1}\\=2y^{1+1}\\\mathrm{Add\:the\:numbers:}\:1+1=2\\=2y^2\\2\cdot \:3y=6y\\2\cdot \:3y\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:3=6\\=6y$

$5\cdot \:3=15\\5\cdot \:3\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:3=15\\=15\\=-2y^2-6y+5y+15\\\mathrm{Add\:similar\:elements:}\:-6y+5y=-y\\=-2y^2-y+15$

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Decreasing interval: Same as the domain; $f(x)$ is decreasing over the entire real line.

End behavior: The range tells you $f(x)>0$ , and you know $f(x)$ is decreasing over its entire domain. This means that $f(x)\to+\infty$ as $x\to-\infty$ , and $f(x)\to0$ and $x\to+\infty$ .

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