Given:
Expression is
[tex](3x+4)^2-(x-10)^2[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex](3x+4)^2-(x-10)^2[/tex]
Using [tex](a+b)^2=a^2+2ab+b^2[/tex] and [tex](a-b)^2=a^2-2ab+b^2[/tex], we get
[tex]=(3x)^2+2(3x)(4)+(4)^2-[(x)^2-2(x)(10)+(10)^2][/tex]
[tex]=9x^2+24x+16-[x^2-20x+100][/tex]
[tex]=9x^2+24x+16-x^2+20x-100[/tex]
On combining like term, we get
[tex]=(9x^2-x^2)+(24x+20x)+(16-100)[/tex]
[tex]=8x^2+44x+(-84)[/tex]
[tex]=8x^2+44x-84[/tex]
Therefore, the correct option is c.
