(2a+3b-3c)的平方等于多少

问题描述:

(2a+3b-3c)的平方等于多少

4a^2+12ab-12ac-18bc+9b^2+9c^2

(x+y+z)^2=x^2+y^2+z^2+2xy+2xz+2yz
所以
(2a+3b-3c)的平方
=(2a)^2+(3b)^2+(-3c)^2+2*2a*3b+2*2a*(-3c)+2*3b*(-3c)
=4a^2+9b^2+9c^2+12ab-12ac-18bc

(2a+3b-3c)^2=(2a+3b)^2+2(2a+3b)(-3c)+(-3c)^2=4a^2+9b^2+9c^2+12ab-12ac-18bc

(2a+3b-3c)^2
=[2a+(3b-3c)]^2
=4a^2+4a(3b-3c)+(3b-3c)^2
=4a^2+12ab-12ac+9b^2-18bc+9c^2

(2a+3b-3c)的平方
=(2a)²+2(2a)(3b-3c)+(3b-3c)²
=4a²+12ab-12ac+9b²-18bc+9c²