Question

Phân tích các đa thức sau thành nhân tử

\(a,\left(x^2+1\right)^2-6\left(x^2+1\right)+9\)

\(b,-25x^6-y^8+10x^3y^4\)

\(c,49\left(y-4\right)^2-9\left(y+2\right)^2\)

Giúp tui gấp !

Answer 1

a, \(\left(x^2+1\right)^2-6\left(x^2+1\right)+9\)

=\(x^4+2x^2+1-6x^2-6+9\)

=\(\left(x^2\right)^2-2.x^2.2+2^2\)

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

b, \(-25x^6-y^8+10x^3y^4\)

= \(-\left(\left(5x^3\right)^2-2.5x^3y^4+\left(y^4\right)^2\right)\)

= \(-\left(5x^3-y^4\right)^2\)

c, \(49\left(y-4\right)^2-9\left(y+2\right)^2\)

=\(\left(7\left(y-4\right)\right)^2-\left(3\left(y+2\right)\right)^2\)

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

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

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

Mình làm hơi tắt cho nhanh nhé :))

Answer 2

sửa phần b)

=(7y-28+3y+6)(7y-28-3y-6)

=(10y-22)(4y-34)