a) (2x+3)²-2(2x+3)(2x+5)+(2x+5)²

=4x²+12x+9-(4x+6)(2x+5)+4x²+20x+25

=4x²+12x+9-(8x²+12x+20x+30)+4x²+20x+25

=4x²+12x+9-8x²-12x-20x-30+4x²+20x+25

=4

b) (x²+x+1)(x²-x+1)(x²-1)

=((x²+1)²-x²)(x²-1)

=(x⁴+x²+1)(x²-1)

=x⁶+x⁴+x²-x⁴-x²-1

=x⁶-1

c)(a+b-c)²+(a-b+c)²-2(b-c)²

=a²+b²+c²+2ab-2ac-2bc+a²+b²+c²-2ab+2ac-2bc-2(b²-2bc+c²)

=2a²+2b²+2c²-4bc-2b²+4bc-2c²

=2a²

d) (a+b+c)²+(a-b-c)²+(b-c-a)²+(c-a-b)²

= a²+b²+c²+2ab+2ac+2bc+a²+b²+c²-2ab-2ac+2bc+a²+b²+c²+2bc-2ab+2ac+a²+b²+c²-2ac-2bc+2ab

=4a²+4b²+4c²+4ab+4bc

d) (a+b+c)²+(a-b-c)²+(b-c-a)²+(c-a-b)²

= a²+b²+c²+2ab+2ac+2bc+a²+b²+c²-2ab-2ac+2bc+a²+b²+c²-2bc-2ab+2ac+a²+b²+c²-2ac-2bc+2ab

=4a²+4b²+4c²

Bài 1:

• a,(2+xy)^2=4+4xy+x^2y^2
• b,(5-3x)^2=25-30x+9x^2
• d,(5x-1)^3=125x^3 - 75x^2 + 15x^2 - 1

Tách ra mỗi câu một lần.

Dài quá không ai làm đâu.

Nhìn nản lắm.

Câu 3: 

a: \(49^2=2401\)

b: \(51^2=2601\)

c: \(99\cdot100=9900\)

a: ĐKXĐ: x<>1/2

Sửa đề: \(A=\frac{3}{2\left(2x-1\right)}\cdot\sqrt{8x^4\left(4x^2-4x+1\right)}\)

\(=\frac{3}{2\left(2x-1\right)}\cdot\sqrt8\cdot\sqrt{x^4}\cdot\sqrt{\left(2x-1\right)^2}\)

\(=\frac{3}{2\left(2x-1\right)}\cdot2\sqrt2\cdot x^2\cdot\left|2x-1\right|=\frac{6\sqrt2\cdot x^2}{2\left(2x-1\right)}\cdot\left|2x-1\right|\)

=\(\pm3\sqrt2\cdot x^2\)

b: ĐKXĐ: b<>0

\(B=\frac{a-b}{b^2}\cdot\sqrt{\frac{a^2b^4}{a^2-2ab+b^2}}\)

\(=\frac{a-b}{b^2}\cdot\sqrt{a^2}\cdot\frac{\sqrt{b^4}}{\sqrt{\left(a-b\right)^2}}\)

\(=\frac{a-b}{b^2}\cdot\left|a\right|\cdot\frac{b^2}{\left|a-b\right|}=\left|a\right|\cdot\frac{a-b}{\left|a-b\right|}=\pm\left|a\right|\)

a) \(A=\left(x+2\right)\left(x^2-2x+4\right)-x^3+2\)

\(A=x^3+8-x^3+2\)

\(A=10\)

b) \(B=\left(x-1\right)\left(x^2+x+1\right)-\left(x+1\right)\left(x^2-x+1\right)\)

\(B=x^3-1-\left(x^3+1\right)\)

\(B=x^3-1-x^3-1\)

\(B=-2\)

c) \(C=\left(2x-y\right)\left(4x^2+2xy+y^2\right)+\left(y-3x\right)\left(y^2+3xy+9x^2\right)\)

\(C=\left(2x\right)^3-y^3+y^3-\left(3x\right)^3\)

\(C=8x^3-y^3+y^3-27x^3\)

\(C=-19x^3\)

a)

\(A=\left(x+2\right)\left(x-2\right)\left(x-2\right)-x^3+2\\ =\left(x^2-4\right)\left(x-2\right)-x^3+2\\ =x^3-2x^2-4x+8-x^3+2\\ =-2x^2-4x+10\)

b)

\(B=x^3-1-\left(x^3+1\right)\\ =x^3-1-x^3-1\\ =-2\)

c)

\(C=\left(2x\right)^3-y^3+\left(y\right)^3-\left(3x\right)^3\\ =8x^3-y^3+y^3-27x^3\\ =-19x^3\)

a) \(\left(3-xy^2\right)^2-\left(2+xy^2\right)^2\)

\(=\left(3-xy^2+2+xy^2\right)\left(3-xy^2-2-xy^2\right)\)

\(=5.\left(-2xy^2\right)\)

\(=-10xy^2\)

b) \(\left(x-y\right)\left(x^2+xy+y^2\right)\)

\(=x^3-y^3\)

c) \(\left(x-3\right)^3+\left(2-x\right)^3\)

\(=x^3-3x^2.3+3x.3^2-3^3+2^3-3.2^2.x+3.2.x^2-x^3\)

\(=x^3-9x^2+27x-27+8-12x+6x^2-x^3\)

\(=\left(x^3-x^3\right)+\left(-9x^2+6x^2\right)+\left(27x-12x\right)+\left(-27+8\right)\)

\(=-3x^2+15x-19\)

bạn viết thế này khó nhìn quá

nhìn hơi đau mắt nhá bạn hoa mắt quá