Question

先化简，再求值：(2a-3b)^2-(2a+3b)(2a-3b)+(2a+3b)^2，a=-2,b=1/3

先化简，再求值：(2a-3b)^2-(2a+3b)(2a-3b)+(2a+3b)^2，a=-2,b=1/3

Answer 1

(2a-3b)^2-(2a+3b)(2a-3b)+(2a+3b)^2
=[(2a-3b)-(2a+3b)]^2+(2a+3b)(2a-3b)
=36b^2+4a^2-9b^2
=27b^2+4a^2
将a=-2,b=1/3代入，
原式=27*(1/3)^2+4*（-2）^2=3+16=19

Answer 2

(2a-3b)²-(2a+3b)(2a-3b)+(2a+3b)²
=4a²-12ab+9b²-(4a²-9b²)+4a²+12ab+9b²
=8a²+18b²-4a²+9b²
=4a²+27b²
当a=-2,b=1/3时
原式=4×(-2)²+27×(1/3)²
=4×4+27×1/9
=16+3
=19

Answer 3

根据公式m^2+n^3=(m+n)(m^2-mn+n^2)
所以：
(2a-3b)^2-(2a+3b)(2a-3b)+(2a+3b)^2
=[(2a-3b)^3+(2a+3b)^3]/[(2a-3b)+(2a+3b)]
=[(-5)^3+(-3)^3]/[(-5)+(-3)]
=(-125-27)/(-8)
=(-152)/(-8)
=19

Answer 4

(2a-3b)^2-(2a+3b)(2a-3b)+(2a+3b)^2
=(2a-3b)(2a-3b-2a-3b)+(2a+3b)^2
=-12ab+18b²+4a²+12ab+9b²
=4a²+27b²
=4*4+27*1/9
=16+3
=19