Question

Phân tích các đa thức sau thành nhân tử

a)25x² - 1

b)x² - 4x + 4 - y²

c)x³ + 8x² + 16x

d)x² - y² - 3x - 3y

e)9x² - y² + 10y - 25

f)x² + 8x + 7

g)3x² - 2x - 5

h)x² - 4x - 5

Answer 1

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

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

\(C=x\left(x^2+8x+16\right)=x\left(x+4\right)^2\)

\(D=\left(x-y\right)\left(x+y\right)-3\left(x+y\right)=\left(x-y-3\right)\left(x+y\right)\)

\(E=\left(3x\right)^2-\left(y^2-10y+25\right)=\left(3x\right)^2-\left(y-5\right)^2\)

\(=\left(3x-y+5\right)\left(3x+y-5\right)\)

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

\(G=3x^2+3x-5x-5=3x\left(x+1\right)-5\left(x+1\right)=\left(x+1\right)\left(3x-5\right)\)

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