Evaluate
b^{2}+c^{2}-d^{2}
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b^{2}+c^{2}-d^{2}
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c^{2}+2cd+d^{2}+b^{2}-2\left(c+d\right)d
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(c+d\right)^{2}.
c^{2}+2cd+d^{2}+b^{2}+\left(-2c-2d\right)d
Use the distributive property to multiply -2 by c+d.
c^{2}+2cd+d^{2}+b^{2}-2cd-2d^{2}
Use the distributive property to multiply -2c-2d by d.
c^{2}+d^{2}+b^{2}-2d^{2}
Combine 2cd and -2cd to get 0.
c^{2}-d^{2}+b^{2}
Combine d^{2} and -2d^{2} to get -d^{2}.
c^{2}+2cd+d^{2}+b^{2}-2\left(c+d\right)d
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(c+d\right)^{2}.
c^{2}+2cd+d^{2}+b^{2}+\left(-2c-2d\right)d
Use the distributive property to multiply -2 by c+d.
c^{2}+2cd+d^{2}+b^{2}-2cd-2d^{2}
Use the distributive property to multiply -2c-2d by d.
c^{2}+d^{2}+b^{2}-2d^{2}
Combine 2cd and -2cd to get 0.
c^{2}-d^{2}+b^{2}
Combine d^{2} and -2d^{2} to get -d^{2}.
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