Respuesta :
Answer:
To obtain an identity replace * by 10 in first equation and * by 15ab in second equation.
Step-by-step explanation:
Monomial is an algebraic expression consisting of one term only.
Given monomial:
1) [tex](*-2m)^2=100-40m+4m^2[/tex]
We have to find the value of * in above equation
Using identity [tex](a-b)^2=a^2-2ab+b^2[/tex]
Comparing with given equation, we get
a= * , b = 2m
then apply the identity, we get
[tex](*-2m)^2=*^2-2 \times 2m \times *+(2m)^2[/tex]
[tex]\Rightarrow (*-2m)^2=*^2-4m*+4m^2[/tex]
now again comparing with the given equation,
[tex]\Rightarrow *^2-4m*+4m^2=100-40m+4m^2[/tex]
This gives * = 10 as [tex]-4m*=-40m \Rightarrow *=10[/tex]
2) [tex](3a+2.5b)^2=9a^2+6.25b^2 + *[/tex]
We have to find the value of * in above equation
Using identity [tex](a+b)^2=a^2+2ab+b^2[/tex]
Comparing with given equation, we get
a= 3a , b = 2.5b
then apply the identity, we get
[tex](3a+2.5b)^2=(3a)^2+(2.5b)^2 + 2 \times 3a \times 2.5b[/tex]
[tex]\Rightarrow (3a+2.5b)^2=(3a)^2+(2.5b)^2 +15ab[/tex]
now again comparing with the given equation, we get * = 15ab
Thus, to obtain an identity replace * by 10 in first equation and * by 15ab in second equation.
