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2 years ago

15

Is 2(5m-4)-3(m-5)^2 equivalent to -3m^2+40m-83? Show your work.

1 answer:

ivann1987 [24]2 years ago

4 0

$\\ \sf\longmapsto 2(5m-4)-3(m-5)^2$

$\\ \sf\longmapsto 10m-8-3(m^2-10m+5^2)$

$\\ \sf\longmapsto 10m-8-3(m^2-10m+25)$

$\\ \sf\longmapsto 10m-8-3m^2+30m-75$

$\\ \sf\longmapsto -3m^2+30m+10m-75-8$

$\\ \sf\longmapsto -3m^2+40m-83$

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Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

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$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

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Therefore, the zeros of our given function are $x=-2,0,3$ .

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