Question #600cc

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Question #600cc

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Answer 1 · 2018-02-13T00:08:58

$(x - 5) (x - 5) (x - 5) = x^{3} - 15 x^{2} + 75 x - 125$ $(x-5)(x-5)(x-5)=x^3-15x^2+75x-125$

Explanation:

First, Let's Use the formula

$(a - b) (a - b) (a - b) = {(a - b)}^{3} = a^{3} - 3 b a^{2} + 3 a b^{2} - b^{3}$ $(a-b)(a-b)(a-b)=(a-b)^3=a^3-3ba^2+3ab^2-b^3$

Then,Subsutite $a = x and b = 5$ $a=x and b=5$ ,so

${(x - 5)}^{3} = x^{3} - (3) (5) x^{2} + 3 (x) (5^{2}) - 5^{3}$ $(x-5)^3=x^3-(3)(5)x^2+3(x)(5^2)-5^3$
$= x^{3} - 15 x^{2} + 75 x - 125$ $=x^3-15x^2+75x-125$

Answer 2 · 2018-02-13T00:09:14

$x^{3} - 15 x^{2} + 75 x - 125$ $x^3-15x^2+75x-125$

Explanation:

Start by expanding the first two terms. You may have learned the FOIL method, where you multiply First, Outer, Inner, then Last terms. Here it is with the first two:
$(x - 5) (x - 5)$ $(x-5)(x-5)$
First: $x \cdot x = x^{2}$ $x*x = x^2$
Outer: $x \cdot - 5 = - 5 x$ $x*-5 = -5x$
Inner: $- 5 \cdot x = - 5 x$ $-5*x = -5x$
Last: $- 5 \cdot - 5 = 25$ $-5*-5 = 25$

Now add the like terms together.
$x^{2} - 5 x - 5 x + 25$ $x^2 -5x-5x+25$
$x^{2} - 10 x + 25$ $x^2-10x+25$

Now multiply that trinomial by the final binomial:
$x^{2} \cdot x = x^{3}$ $x^2*x = x^3$
$x^{2} \cdot - 5 = - 5 x^{2}$ $x^2*-5 = -5x^2$
$- 10 x \cdot x = - 10 x^{2}$ $-10x*x = -10x^2$
$- 10 x \cdot - 5 = 50 x$ $-10x*-5 = 50x$
$25 \cdot x = 25 x$ $25*x = 25x$
$25 \cdot - 5 = - 125$ $25*-5 = -125$

Again, add all like terms together to get your final answer.
$x^{3} - 5 x^{2} - 10 x^{2} + 50 x + 25 x - 125$ $x^3-5x^2-10x^2+50x+25x-125$

$x^{3} - 15 x^{2} + 75 x - 125$ $x^3-15x^2+75x-125$

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Question #600cc

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