Evaluate
\left(5x+2y\right)^{2}+12y^{2}-3
Expand
25x^{2}+20xy+16y^{2}-3
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25x^{2}+20xy+4y^{2}-3\left(1+2y\right)\left(1-2y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+2y\right)^{2}.
25x^{2}+20xy+4y^{2}+\left(-3-6y\right)\left(1-2y\right)
Use the distributive property to multiply -3 by 1+2y.
25x^{2}+20xy+4y^{2}-3+12y^{2}
Use the distributive property to multiply -3-6y by 1-2y and combine like terms.
25x^{2}+20xy+16y^{2}-3
Combine 4y^{2} and 12y^{2} to get 16y^{2}.
25x^{2}+20xy+4y^{2}-3\left(1+2y\right)\left(1-2y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+2y\right)^{2}.
25x^{2}+20xy+4y^{2}+\left(-3-6y\right)\left(1-2y\right)
Use the distributive property to multiply -3 by 1+2y.
25x^{2}+20xy+4y^{2}-3+12y^{2}
Use the distributive property to multiply -3-6y by 1-2y and combine like terms.
25x^{2}+20xy+16y^{2}-3
Combine 4y^{2} and 12y^{2} to get 16y^{2}.
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