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a) (2x - 1)2 - (x + 3)2
= (2x - 1 - x - 3).(2x - 1 + x + 3)
= (x - 4).(3x + 2)
b) x2.(x - 3) + 12 - 4x
= x2.(x - 3) - 4x + 12
= x2.(x - 3) - 4.(x - 3)
= (x - 3).(x2 - 4)
= (x - 3).(x - 2).(x + 2)
Áp dụng HĐT:
a2 - b2 = (a - b)(a + b)
\(\left(2x-1\right)^2-\left(x+3\right)^2\)
\(=\left(2x-1-x-3\right)\left(2x-1+x+3\right)\)
\(=\left(x-4\right)\left(3x+2\right)\)
a) Đề đúng: \(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=\left(x^2+x\right)+4\left(x^2+x\right)-12\)
Đặt \(x^2+x=y\)
BT = \(y^2+4y-12\)
\(=\left(y+2\right)^2-4^2\)
\(=\left(y-2\right)\left(y+6\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x-6\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x-2\right)\left(x+3\right)\)
b) Đặt \(x^2+x+1=y\)
=> BT = \(y\left(y+1\right)-12\)
\(=y^2+y-12\)
\(=\left(y-3\right)\left(y+4\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+6\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
a) \(x^2-6x+8\)
\(=x^2-6x+9-1\)
\(=\left(x^2-6x+9\right)-1\)
\(=\left(x-3\right)^2-1\)
\(=\left(x-3-1\right)\left(x-3+1\right)\)
\(=\left(x-4\right)\left(x-2\right)\)
a) (x2 + x)2 + 4x2 + 4x - 12
= x4 + 2x3 + x2 + 4x2 + 4x - 12
= x4 + 2x3 + 5x2 + 4x - 12
= x4 - x3 + 3x3 - 3x2 + 8x2 - 8x + 12x - 12
= x3(x - 1) + 3x2(x - 1) + 8x(x - 1) + 12(x - 1)
= (x - 1)(x3 + 3x2 + 8x + 12)
= (x - 1)(x3 + 2x2 + x2 + 2x + 6x + 12)
= (x - 1)[x2(x + 2) + x(x + 2) + 6(x + 2)]
= (x - 1)(x + 2)(x2 + x + 6)
b) (x2 + x + 1)(x2 + x + 2) - 12 (*)
Đặt x2 + x + 1 = t, ta có:
(*) = t(t + 1) - 12
= t2 + t - 12
= t2 - 3t + 4t - 12
= t(t - 3) + 4(t - 3)
= (t - 3)(t + 4)
= (x2 + x + 1 - 3)(x2 + x + 1 + 4)
= (x2 + x - 2)(x2 + x + 5)
= (x2 - x + 2x - 2)(x2 + x + 5)
= [x(x - 1) + 2(x - 1)](x2 + x + 5)
= (x - 1)(x + 2)(x2 + x + 5)