Question

Phân tích đa thức thành nhân tử : a, 36a^2 - ( a^2 + 9 )^2

b, (a + 3b ) ^2 - ( a^2 + 9 ) ^2

c, 9(2a - x ) ^2 - 4(3a-x)^2

d, x^5 - x^3 + x^2 -1/5

e, x^4 + x^3 + x + 1

Answer 1

Phân tích đa thức thành nhân tử:

a, \(36a^2-\left(a^2+9\right)^2\)

\(=\left(6a\right)^2-\left(a^2+9\right)^2\)

\(=\left(6a-a^2-9\right)\left(6a+a^2+9\right)\)

b, \(\left(a+3b\right)^2-\left(a^2+9\right)^2\)

\(=\left(a+3b-a^2-9\right)\left(a+3b+a^2+9\right)\)

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

\(=\left[3\left(2a-x\right)\right]^2-\left[2\left(3a-x\right)\right]^2\)

\(=\left(6a-3x\right)^2-\left(6a-2x\right)^2\)

\(=\left(6a-3x-6a+2x\right)\left(6a-3x+6a-2x\right)\)

\(=\left(-x\right)\left(12a-5x\right)\)

e, \(x^4+x^3+x+1\)

\(=\left(x^4+x^3\right)+\left(x+1\right)\)

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

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