Răspuns:
[tex]\boldsymbol{ \red{E(x) = 4x^2 - 6x + 3 }}[/tex]
Explicație pas cu pas:
Desfacem parantezele, apoi reducem termenii asemenea:
E(x) = (x+4)²-2(2-x)(2x-3)-(x-3)²-2(3x+8)
= x²+8x+4²-2(4x-6-2x²+3x)-(x²-6x+3²)-6x-16
= x²+8x+16+4x²-14x+12-x²+6x-9-6x-16
= (x²+4x²-x²)+(8x-14x+6x-6x)+(16+12-9-16)
[tex]= 4x^2 - 6x + 3[/tex]
Formule de calcul prescurtat:
[tex]\boxed{\boxed{\boldsymbol{(a \pm b)^{2} = a^{2} \pm 2ab + b^{2}}} \ \ \boxed{\boldsymbol{(a - b)(a + b) = a^{2} - b^{2}}}}\\[/tex]
