1)
a/ $\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)$
$=\left(x-2\right)\left(x^2+2x+2^2\right)-\left(x^3+3x^2+3x+1\right)+\left(3x-3\right)\left(x+1\right)$
$=\left(x^3-2^3\right)-x^3-3x^2-3x-1+3x\left(x+1\right)-3\left(x+1\right)$
$=-3x-6$
b/ $\left(x^4-5x^2+25\right)\left(x^2+5\right)-\left(2+x^2\right)^2+3\left(1+x^2\right)^2$
= $\left[\left(x^2\right)^2-5x^2+5^2\right]\left(x^2+5\right)-\left[2^2-2.2x^2+\left(x^2\right)^2\right]+3\left(1^2+2.x^2+x^4\right)$
= $\left[\left(x^2\right)^3+5^3\right]-\left(4-4x^2+x^4\right)+3+6x^2+3x^4$
$=2x^4+x^6+124+10x^2$
2:
a/ $\left(5x+1\right)^2-\left(5x+3\right)\left(5x-3\right)=30$
$\Rightarrow \left[\left(5x\right)^2+2.5x+1^2\right]-\left[\left(5x\right)^2-3^2\right]=30$
$\Rightarrow \left(25x^2+10x+1\right)-\left(25x^2-9\right)=30$
$\Rightarrow 25x^2+10x+1-25x^2+9=30$
$\Rightarrow 10x+10=30$
=> 10x = 30 - 10 = 20
=> x = 20 : 10 = 2
b/ $\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)=15$
$\Rightarrow x^3+3^3-x\left(x^2-2^2\right)=15$
$\Rightarrow x^3+27-x^3+4x=15$
$\Rightarrow 4x=15-27=-12$
$\Rightarrow x=\left(-12\right):4=-3$
