Question

Answer 1

Bài 2:

a: \(5x^2-10x+25=5\cdot x^2-5\cdot2x+5\cdot5=5\left(x^2-2x+5\right)\)

b: \(3x^2y-\frac32x^3y^2+6xy\)

\(=3xy\cdot x-3xy\cdot\frac12x^2y+3xy\cdot2\)

\(=3xy\cdot\left(x-\frac12x^2y+2\right)\)

c: \(4x^2\left(3x-2\right)-9\left(3x-2\right)\)

\(=\left(3x-2\right)\left(4x^2-9\right)\)

=(3x-2)(2x-3)(2x+3)

d: \(7x^2\left(x+1\right)-14x\left(x+1\right)\)

\(=\left(x+1\right)\left(7x^2-14x\right)\)

=7x(x-2)(x+1)

e: \(x^4\left(2x-1\right)+16\left(1-2x\right)\)

\(=x^4\left(2x-1\right)-16\left(2x-1\right)\)

\(=\left(2x-1\right)\cdot\left(x^4-16\right)=\left(2x-1\right)\left(x^2+4\right)\left(x^2-4\right)\)

\(=\left(2x-1\right)\left(x^2+4\right)\left(x-2\right)\left(x+2\right)\)

f: \(5x^3-10x^2+5x\)

\(=5x\left(x^2-2x+1\right)\)

\(=5x\left(x-1\right)^2\)

Bài 3:

a: \(x^2-22x+121=x^2-2\cdot x\cdot11+11^2\)

\(=\left(x-11\right)^2\)

b: \(25xy^2-20xy+4x\)

\(=x\left(25y^2-20y+4\right)\)

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

c: \(49-14x+x^2=7^2-2\cdot7\cdot x+x^2=\left(7-x\right)^2\)

d: \(x^2-81=x^2-9^2=\left(x-9\right)\left(x+9\right)\)

e: \(16x^2-9=\left(4x\right)^2-3^2=\left(4x-3\right)\left(4x+3\right)\)

f: \(x^4-4=\left(x^2\right)^2-2^2=\left(x^2-2\right)\left(x^2+2\right)\)

g: \(x^3-\frac18=x^3-\left(\frac12\right)^3=\left(x-\frac12\right)\left(x^2+\frac12x+\frac14\right)\)

h: \(8x^3+125=\left(2x\right)^3+5^3=\left(2x+5\right)\left(4x^2-10x+25\right)\)

k: \(x^3+6x^2+12x+8\)

\(=x^3+3\cdot x^2\cdot2+3\cdot x\cdot2^2+2^3\)

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