Evaluate
\left(y-5\right)\left(y+3\right)^{2}
Expand
y^{3}+y^{2}-21y-45
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\left(y-5\right)\left(y+3\right)^{2}
Multiply y+3 and y+3 to get \left(y+3\right)^{2}.
\left(y-5\right)\left(y^{2}+6y+9\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+3\right)^{2}.
y^{3}+6y^{2}+9y-5y^{2}-30y-45
Apply the distributive property by multiplying each term of y-5 by each term of y^{2}+6y+9.
y^{3}+y^{2}+9y-30y-45
Combine 6y^{2} and -5y^{2} to get y^{2}.
y^{3}+y^{2}-21y-45
Combine 9y and -30y to get -21y.
\left(y-5\right)\left(y+3\right)^{2}
Multiply y+3 and y+3 to get \left(y+3\right)^{2}.
\left(y-5\right)\left(y^{2}+6y+9\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+3\right)^{2}.
y^{3}+6y^{2}+9y-5y^{2}-30y-45
Apply the distributive property by multiplying each term of y-5 by each term of y^{2}+6y+9.
y^{3}+y^{2}+9y-30y-45
Combine 6y^{2} and -5y^{2} to get y^{2}.
y^{3}+y^{2}-21y-45
Combine 9y and -30y to get -21y.
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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