<span>Equation at the end of step 1 :</span><span> (24x2 + 40x) + 25
</span><span>Step 2 :</span>Trying to factor by splitting the middle term
<span> 2.1 </span> Factoring <span> 16x2+40x+25</span>
The first term is, <span> <span>16x2</span> </span> its coefficient is <span> 16 </span>.
The middle term is, <span> +40x </span> its coefficient is <span> 40 </span>.
The last term, "the constant", is <span> +25 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 16</span> • 25 = 400</span>
Step-2 : Find two factors of 400 whose sum equals the coefficient of the middle term, which is <span> 40 </span>.
<span><span> -400 + -1 = -401</span><span> -200 + -2 = -202</span><span> -100 + -4 = -104</span><span> -80 + -5 = -85</span><span> -50 + -8 = -58</span><span> -40 + -10 = -50</span><span> -25 + -16 = -41</span><span> -20 + -20 = -40</span><span> -16 + -25 = -41</span><span> -10 + -40 = -50</span><span> -8 + -50 = -58</span><span> -5 + -80 = -85</span><span> -4 + -100 = -104</span><span> -2 + -200 = -202</span><span> -1 + -400 = -401</span><span> 1 + 400 = 401</span><span> 2 + 200 = 202</span><span> 4 + 100 = 104</span><span> 5 + 80 = 85</span><span> 8 + 50 = 58</span><span> 10 + 40 = 50</span><span> 16 + 25 = 41</span><span> 20 + 20 = 40 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 20 and 20
<span>16x2 + 20x</span> + 20x + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (4x+5)
Add up the last 2 terms, pulling out common factors :
5 • (4x+5)
Step-5 : Add up the four terms of step 4 :
(4x+5) • (4x+5)
Which is the desired factorization
Multiplying Exponential Expressions :
<span> 2.2 </span> Multiply (4x+5) by (4x+5)
The rule says : To multiply exponential expressions which have the same base,<span> add up their exponents.</span>
In our case, the common base is (4x+5) and the exponents are :
1 , as (4x+5) is the same number as <span> (4x+5)1</span>
and 1 , as (4x+5) is the same number as <span> (4x+5)1</span>
The product is therefore, <span> (4x+5)<span>(1+1)</span> = (4x+5)2</span>
Final result :<span> (4x + 5)<span>2
hope this helps hope i am brainliest i need it
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