Question

Answer 1

a) \(x^2-6xy+9y^2=x^2-2.3.x.y+\left(3y\right)^2=\left(x-3y\right)^2\)

b) \(x^3+6x^2y+12xy^2+8y^3=x^3+3.2.x^2y+3.x.\left(2y\right)^2+\left(2y\right)^3=\left(x+2y\right)^3\)

c) \(x^3-64=x^3-4^3=\left(x-4\right)\left(x^2+4x+16\right)\)

d) \(125x^3+y^6=\left(5x\right)^3+\left(y^2\right)^3=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\)

e)

 \(0,125\left(a+1\right)^3-1\\ =\left[0,5.\left(a+1\right)\right]^3-1^3\\ =\left(0,5a+0,5\right)^3-1^3\\ =\left(0,5a+0,5-1\right)\left[\left(0,5a+0,5\right)^2+\left(0,5a+0,5\right).1+1^2\right]\\ =\left(0,5a-0,5\right)\left(0,25a^2+0,5a+0,25+0,5a+0,5+1\right)\\ =\left(0,5a-0,5\right)\left(0,25a^2+a+1,75\right)\)

Answer 2

Bài 5: 

a) Ta có: \(\left(2x+1\right)^2-\left(x-1\right)^2\)

\(=\left(2x+1-x+1\right)\left(2x+1+x-1\right)\)

\(=3x\left(x+2\right)\)

b: Ta có: \(9\left(x+5\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)

\(=\left(2x+22\right)\left(4x+8\right)\)

\(=8\left(x+11\right)\left(x+2\right)\)

c: Ta có: \(25\left(x-y\right)^2-16\left(x+y\right)^2\)

\(=\left(5x-5y\right)^2-\left(4x+4y\right)^2\)

\(=\left(5x-5y-4x-4y\right)\left(5x-5y+4x+4y\right)\)

\(=\left(x-9y\right)\left(9x-y\right)\)

d: Ta có: \(49\left(y-4\right)^2-9\left(y+2\right)^2\)

\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)

\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)\)

\(=\left(4y-34\right)\left(10y-22\right)\)

\(=4\left(2y-17\right)\left(5y-11\right)\)

Answer 3

Bài 4:

a) \(2x\left(x+1\right)+2\left(x+1\right)=2\left(x+1\right)^2\)

b: \(y^2\left(x^2+y\right)-x^2z-yz\)

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

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

c: \(4x\left(x-2y\right)+8y\left(2y-x\right)\)

\(=4x\left(x-2y\right)-8y\left(x-2y\right)\)

\(=4\left(x-2y\right)^2\)