Mister Exam
Factor t^2+4*t*x+3*x^2 squared
The solution
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2 2 t + 4*t*x + 3*x
$$3 x^{2} + \left(t^{2} + 4 t x\right)$$
t^2 + (4*t)*x + 3*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$3 x^{2} + \left(t^{2} + 4 t x\right)$$
Let us write down the identical expression
$$3 x^{2} + \left(t^{2} + 4 t x\right) = - x^{2} + \left(t^{2} + 4 t x + 4 x^{2}\right)$$
or
$$3 x^{2} + \left(t^{2} + 4 t x\right) = - x^{2} + \left(t + 2 x\right)^{2}$$
in the view of the product
$$\left(- \sqrt{1} x + \left(t + 2 x\right)\right) \left(\sqrt{1} x + \left(t + 2 x\right)\right)$$
$$\left(- x + \left(t + 2 x\right)\right) \left(x + \left(t + 2 x\right)\right)$$
$$\left(t + x \left(-1 + 2\right)\right) \left(t + x \left(1 + 2\right)\right)$$
$$\left(t + x\right) \left(t + 3 x\right)$$
$$3 x^{2} + \left(t^{2} + 4 t x\right)$$
Let us write down the identical expression
$$3 x^{2} + \left(t^{2} + 4 t x\right) = - x^{2} + \left(t^{2} + 4 t x + 4 x^{2}\right)$$
or
$$3 x^{2} + \left(t^{2} + 4 t x\right) = - x^{2} + \left(t + 2 x\right)^{2}$$
in the view of the product
$$\left(- \sqrt{1} x + \left(t + 2 x\right)\right) \left(\sqrt{1} x + \left(t + 2 x\right)\right)$$
$$\left(- x + \left(t + 2 x\right)\right) \left(x + \left(t + 2 x\right)\right)$$
$$\left(t + x \left(-1 + 2\right)\right) \left(t + x \left(1 + 2\right)\right)$$
$$\left(t + x\right) \left(t + 3 x\right)$$
Combining rational expressions
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2 3*x + t*(t + 4*x)
$$t \left(t + 4 x\right) + 3 x^{2}$$
3*x^2 + t*(t + 4*x)