<span><span> ((8p3+16p2)/(20p+40))/((2p-10)/(2p2-12p+10))</span> </span>Final result :<span> 2p2 • (p - 1)
—————————————
5
</span>
Step by step solution :<span>Step 1 :</span>Skip Ad
<span>Equation at the end of step 1 :</span><span> ((8•(p3))+(16•(p2))) (2p-10)
———————————————————— ÷ ——————————————
(20p+40) ((2p2-12p)+10)
</span><span>Step 2 :</span><span> 2p - 10
Simplify ——————————————
2p2 - 12p + 10
</span><span>Step 3 :</span>Pulling out like terms :
<span> 3.1 </span> Pull out like factors :
2p - 10 = 2 • (p - 5)
<span>Step 4 :</span>Pulling out like terms :
<span> 4.1 </span> Pull out like factors :
<span> 2p2 - 12p + 10</span> = <span> 2 • (p2 - 6p + 5)</span>
Trying to factor by splitting the middle term
<span> 4.2 </span> Factoring <span> p2 - 6p + 5</span>
The first term is, <span> <span>p2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -6p </span> its coefficient is <span> -6 </span>.
The last term, "the constant", is <span> +5 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • 5 = 5</span>
Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is <span> -6 </span>.
<span> -5 + -1 = -6 That's it</span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
<span>p2 - 5p</span> - 1p - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (p-5)
Add up the last 2 terms, pulling out common factors :
1 • (p-5)
Step-5 : Add up the four terms of step 4 :
(p-1) • (p-5)
Which is the desired factorization
Canceling Out :
<span> 4.3 </span> Cancel out <span> (p-5) </span> which appears on both sides of the fraction line.
<span>Equation at the end of step 4 :</span><span><span> ((8•(p3))+(16•(p2))) 1
———————————————————— ÷ ———
(20p+40) p-1
</span><span> Step 5 :</span></span><span>Equation at the end of step 5 :</span><span><span> ((8•(p3))+24p2) 1
——————————————— ÷ ———
(20p+40) p-1
</span><span> Step 6 :</span></span><span>Equation at the end of step 6 :</span><span> (23p3 + 24p2) 1
————————————— ÷ —————
(20p + 40) p - 1
</span><span>Step 7 :</span><span> 8p3 + 16p2
Simplify ——————————
20p + 40
</span><span>Step 8 :</span>Pulling out like terms :
<span> 8.1 </span> Pull out like factors :
<span> 8p3 + 16p2</span> = <span> 8p2 • (p + 2)</span>
<span>Step 9 :</span>Pulling out like terms :
<span> 9.1 </span> Pull out like factors :
20p + 40 = 20 • (p + 2)
Canceling Out :
<span> 9.2 </span> Cancel out <span> (p + 2) </span> which appears on both sides of the fraction line.
<span>Equation at the end of step 9 :</span><span> 2p2 1
——— ÷ —————
5 p - 1
</span><span>Step 10 :</span><span> 2p2 1
Divide ——— by —————
5 (p-1)
</span>
<span> 10.1 </span> Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
<span><span>2p2 1 2p2 p - 1
——— ÷ ——————— = ——— • —————
5 (p - 1) 5 1
</span>
</span>Final result :<span> 2p2 • (p - 1)
—————————————
5
</span><span>
</span>