MULTIPLICATION
Question: What must be multiplied to [tex](x+5)[/tex] to get [tex]x^{2} -25[/tex]?
Representation:
Let [tex]y[/tex] be the unknown number
Equation:
[tex]{\tt{(x+5)(y)=x^{2} -25}}[/tex]
Solution:
[tex]{\tt{(x+5)(y)=x^{2} -25}}\\{\tt{\frac{(x+5)y}{x+5}= \frac{x^{2}}{x+5}+ \frac{-25}{x+5} }}\\{\tt{y=\frac{x^{2}}{x+5}+ \frac{-25}{x+5} }}\\{\tt{y=\frac{x^{2}-25}{x+5} }}\\{\tt{y=\frac{x^{2}-5^{2}}{x+5} }}\\{\tt{y=\frac{(x+5)(x-5)}{x+5} }}\\{\boxed{\tt{y=(x-5)}}}[/tex]
Answer:
[tex]{\purple{\boxed{\purple{\huge{\boxed{\sf{x-5}}}}}}}[/tex]
Checking:
[tex]{\tt{(x+5)(x-5)}}\\{\tt{x(x)=x^{2} }}\\{\tt{x(-5)=-5x}}\\{\tt{5(x)=5x}}\\{\tt{5(-5)=-25}}\\{\tt{x^{2} -5x+5x-25}}\\{\boxed{\tt{x^{2} -25}}}[/tex]
[tex]{\blue{\boxed{ItzyMidzy:))}}}[/tex]
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