Question

(7+6w+5w^2)(6+5w+7w^2)=??
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Answer 1

Answer:

here, first multiply 7 with 6 , 5w and 7w²

      then we multiply 6w with 6 , 5w and 7w²

       then 5w² with 6 , 5w and 7w²

so basically we are just distributing the products with each term and then adding them up keeping in mind the sign of the terms.. here all are positive so we dont have to be extra careful of the sign :)

lets get into it now...

(7+6w+5w^2)(6+5w+7w^2)

= 7*6 + 7*5w + 7* 7w²+ 6w*6 + 6w*5w + 6w*7w² + 5w² * 6 + 5w² *5w +  

    5w² * 7w ²

= 42 +35w + 49w² + 36w + 30w² + 42w^3 +30w² + 25w^3 + 35w^4

(now add all the like terms)

[= 42 + 35w + 36w + .... ............. ( group them this way) ]

= 42 +71w + 109w² +67w^3 + 35w^4

so now we have a polynomial of degree 4 as final result

i.e answer is

42 + 71w + 109w² +67w^3 + 35w^4

now to make things more clear so that you can do more questions like this..

you see, if you take the case of ( a+b )c ,

we can distribute this like (a+b)c = c*a + c*b

same way, (a+b+c)d = ad + bd + cd

so now come to our question, if you take (6+5w+7w^2) = A -------- equ (1)

then see..

(7+6w+5w^2)(6+5w+7w^2)= (7+6w+5w^2)A

now distribute with A it becomes

7A + 6w*A + 5w^2 * A

i know that by now you've guessed out what im trying to say... :)

so now put the value of A back in from equ (1)

then it becomes

7 (6+5w+7w^2) + 6w (6+5w+7w^2) + 5w^2(6+5w+7w^2)

now just apply distribution to each term here

then we will get

= 7*6 + 7*5w + 7* 7w²+ 6w*6 + 6w*5w + 6w*7w² + 5w² * 6 + 5w² *5w +  

    5w² * 7w ²

(which is what we did above)

now continue... to the answer

hope this helps...

Answer 2

Answer:

2 • (2w - 1) • (3w - 1)

this the answer of this

hope it helped you

Step-by-step explanation: