Toán Lớp 8: Rút gọn: a,(a+b)^3+(a-b)^3-2a^2(a+1) b,(2x-1)^3-(2x+1)^3-5x(x-3) c,(x+2)^3+(x-2)^3-2x(x^2+12) d,(2a+3b)^3-(2a-3b)^3+3(2a-b)(2a+b)

Question

Toán Lớp 8:  Rút gọn: a,(a+b)^3+(a-b)^3-2a^2(a+1) b,(2x-1)^3-(2x+1)^3-5x(x-3) c,(x+2)^3+(x-2)^3-2x(x^2+12) d,(2a+3b)^3-(2a-3b)^3+3(2a-b)(2a+b)

thanoanghha · Answer

Lời giải :

a,(a+b)^3+(a-b)^3-2a^2(a+1)

=a^3+b^3+3.a^2. b+ 3.ab^2+a^3-3.a^2b+3.ab^3-b^3-2a^3-2a^2

=6ab^2-2a^2
b,(2x-1)^3-(2x+1)^3-5x(x-3)

=8x^3-3.4x^2 .1+3.2x.1^2-1-(8x^3+3.4x^2. 1+3.2x.1^2+1)-5x^2+15

=8x^3-12x^2+6x-1-8x^3-12x^2-6x-1-5x^2+15

=-29x^2+13

c,(x+2)^3+(x-2)^3-2x(x^2+12)

=x^3+6x^2+12x+8+x^3-6x^2+12x-8-2x^3-24x

=0
d,(2a+3b)^3-(2a-3b)^3+3(2a-b)(2a+b)

=8a^3+36a^2b+54ab^2+27b^3-(8a^3-36a^2b+54ab^2-27b^3)+3(4a^2-b^2)

=8a^3+36a^2b+54ab^2+27b^3-8a^3+36a^2b-54ab^2+27b^3+12a^2-3b^2

=72a^2b+54b^3+12a^2-3b^2

lanthuhoa · Answer

R&uacute;t gọn:     a,(a+b)^3+(a-b)^3-2a^2(a+1)     = a^3 + 3a^2 b + 3ab^2 + b^3 + a^3 - 3a^2 b + 3ab^2 - b^3 - 2a. 2a(a+1)     = 2a^3 + 6ab^2 - 2a^2(a+1)     b,(2x-1)^3-(2x+1)^3-5x(x-3)     = (2x)^3 - 3.(2x)^2.1 + 3.2x.1^2 - 1^3 -[ (2x)^3 +3.(2x)^2 .1 + 3.2x.1^2 + 1^3] - 5x^2 - 15x     = 8x^3 - 12x^2 + 6x - 1 - 8x^3 - 12x^2 - 6x - 1 - 5x^2 - 15x     = -24x^2 - 5x^2 - 13x     = -29x^2 - 13x     c,(x+2)^3+(x-2)^3-2x(x^2+12)     = x^3 + 3x^2 .2 + 3x.2^2 + 2^2 + (x^3 - 3x^2 .2 + 3x.2^2 - 2^3) - 2x^3 + 24x     = x^3 + 3x^2 .2 + 3x.2^2 + 2^2 + x^3 + 3x^2 .2 - 3x.2^2 + 2^3 - 2x^3 + 24x     = 0     d,(2a+3b)^3-(2a-3b)^3+3(2a-b)(2a+b)     = 8a^3 + 36a^2b + 54ab^2 + 27b^3 - (8a^3 - 36a^2b + 54ab^2 - 27b^3) + 3(4a^2 - b^2)    = 8a^3 + 36a^2 b + 54ab^2 + 27b^3 - 8a^3 + 36a^2 b - 54ab^2 + 27b^3 + 12a^2 - 3b^2   = 72a^2b+54b^3+12a^2-3b^2