18/08/2025
19/08/2025
$(a+b)2=a^2+2ab+b^2$
VD $(3+2)^2=3^2+2⋅3⋅2+2^2=9+12+4=25$
$(a-b)2=a^2-2ab+b^2$
VD $(5−1)^2=5^2−2⋅5⋅1+1^2=25−10+1=16$
$a^2−b^2=(a−b)(a+b)$
VD $9^2−4^2=(9−4)(9+4)=5⋅13=65$
$(a+b)^3=a^3+3a^2b+3ab^2+b^3$
VD $(1+2)^3=1^3+3⋅1^2⋅2+3⋅1⋅2^2+2^3=1+6+12+8=27$
$(a−b)^3=a^3−3a^2b+3ab^2−b3$
VD $(4−1)^3=4^3−3⋅4^2⋅1+3⋅4⋅1^2−1^3=64−48+12−1=27$
$a^3+b^3=(a+b)(a^2−ab+b^2)$
VD $2^3+1^3=(2+1)(2^2−2⋅1+1^2)=3⋅(4−2+1)=3⋅3=9$
$a^3−b^3=(a−b)(a^2+ab+b^2)$
VD $3^3−1^3=(3−1)(3^2+3⋅1+1^2)=2⋅(9+3+1)=2⋅13=26$
19/08/2025
1/ $\left(A+B\right)^2=A^2+2AB+B^2$
$\left(x+2\right)^2=x^2+4x+4$
2/ $\left(A-B\right)^2=A^2-2AB+B^2$
$\left(x-1\right)^2=x^2-2x+1$
3/ $A^2-B^2=\left(A-B\right)\left(A+B\right)$
$x^2-4=\left(x-2\right)\left(x+2\right)$
4/ $\left(A+B\right)^3=A^3+3A^2B+3AB^2+B^3$
$\left(x+2\right)^3=x^3+6x^2+12x+8$
5/ $\left(A-B\right)^3=A^3-3A^2B+3AB^2-B^3$
$\left(x-2\right)^2=x^3-6x^2+12x-8$
6/ $A^3+B^3=\left(A+B\right)\left(A^2-AB+B^2\right)$
$x^3+8=\left(x+2\right)\left(x^2-2x+4\right)$
7/ $A^3-B^3=\left(A-B\right)\left(A^2+AB+B^2\right)$
$x^3-27=\left(x-3\right)\left(x^2+3x+9\right)$.
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