Evaluate
x\left(5x+12\right)
Expand
5x^{2}+12x
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4x^{2}+12x+9-\left(3-x\right)\left(x+3\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.
4x^{2}+12x+9-\left(9-x^{2}\right)
Consider \left(3-x\right)\left(x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.
4x^{2}+12x+9-9+x^{2}
To find the opposite of 9-x^{2}, find the opposite of each term.
4x^{2}+12x+x^{2}
Subtract 9 from 9 to get 0.
5x^{2}+12x
Combine 4x^{2} and x^{2} to get 5x^{2}.
4x^{2}+12x+9-\left(3-x\right)\left(x+3\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.
4x^{2}+12x+9-\left(9-x^{2}\right)
Consider \left(3-x\right)\left(x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.
4x^{2}+12x+9-9+x^{2}
To find the opposite of 9-x^{2}, find the opposite of each term.
4x^{2}+12x+x^{2}
Subtract 9 from 9 to get 0.
5x^{2}+12x
Combine 4x^{2} and x^{2} to get 5x^{2}.
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