Answer:
[tex]100 x^{2}-49 y^{2}[/tex] can be written in the difference of squares.
Option: D
Step-by-step explanation:
We know that [tex]a^{2}-b^{2}=(a-b)(a+b)[/tex]
Take the equation [tex]100 x^{2}-49 y^{2}[/tex] and can be written as follows.
[tex]\left(100 x^{2}-49 y^{2}\right)=\left\{(10 x)^{2}-(7 y)^{2}\right\}[/tex]
100 is the square of 10
49 is the square of 7
[tex]x^{2}[/tex] is the square of x
[tex]y^{2}[/tex] is the square of y
Thus we can write the [tex]100 x^{2}-49 y^{2}[/tex] as the difference of squares.
[tex]\left(100 x^{2}-49 y^{2}\right)=\left\{(10 x)^{2}-(7 y)^{2}\right\}[/tex]
By using the formula [tex]a^{2}-b^{2}=(a-b)(a+b)[/tex] we can write [tex]\left\{(10 x)^{2}-(7 y)^{2}\right\}[/tex] as
[tex]\left\{(10 x)^{2}-(7 y)^{2}\right\}[/tex] [tex]=(10 x-7 y)(10 x+7 y)[/tex]
