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, $x^4+x^3+x+1$

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

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

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

(a^2+a-1)^2 + 4a^2 + 4a

Đặt A = (a^2 + a - 1)^2 + 4a^2 + 4a = (a^2 + a - 1)^2 + 4(a^2 + a)
Đặt a^2 + a = x
=> A = (x - 1)^2 + 4x = x^2 + 2x + 1 = (x + 1)^2 = (a^2 + a + 1)^2

3. PTDTTNT

a) x^16 - 1

b) x^36 - 64

C) x^6 + y^6

d) a. ( x+5 ) . ( x+6 ) . ( x+10 ) . ( x+1 ) - 3x^2

Phân tích đa thức thành nhân tử:

a $x^{16}-1$

$=\left(x^8\right)^2-1^2$

$=\left(x^8-1\right)\left(x^8+1\right)$

b, $x^{36}-64$

$=\left(x^{18}\right)^2-8^2$

$=\left(x^{18}-8\right)\left(x^{18}+8\right)$

$=\left[\left(x^6\right)^3-2^3\right]\left[\left(x^6\right)^3+2^3\right]$

$=\left(x-2\right)\left(x^{12}+2x+4\right)\left(x+2\right)\left(x^{12}-2x+4\right)$

c, $x^6+y^6$

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

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