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\(3x^2-5x+2\)
\(=3x^2-3x-2x+2\)
\(=3x\left(x-1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-2\right)\)
Đề sai rồi bạn phải + 2 chứ
19. 3x2-4x+1
= 3x2-3x-x+1
= (3x2-3x)-(x-1)
= 3x(x-1)-(x-1)
= (3x-1)(x-1)
20.3x2+4x-7
= 3x2+3x-7x-7
= (3x2+3x)-(7x+7)
= 3x(x+1)-7(x-1)
= (3x-7)(x-1)
21.3x2+7x-6
= 3x2+9x-2x-6
= (3x2+9x)-(2x+6)
= 3x(x+3)-2(x+3)
= (3x-2)(x+3)
22.3x2+3x-6
= 3x2+6x-3x-6
=(3x2+6x)-(3x+6)
= 3x(x+2)-3(x+2)
=(3x-3)(x+2)
= 3(x-1)(x+2)
23. 3x2-3x-6
=(3x2-6x)+(3x-6)
=3x(x-2)+3(x-2)
=(3x+3)(x-2)
= 3(x+1)(x-2)
24.6x2-13x+6
= 6x2-9x-4x+6
= (6x2-9x)-(4x-6)
=3x(2x-3)-2(2x-3)
=(3x-2)(2x-3)
25.6x2+13x+6
= 6x2+9x+4x+6
= (6x2+9x)+(4x+6)
=3x(2x+3)+2(2x+3)
=(3x+2)(2x+3)
26. 6x2+15x+6
= (6x2+12x)+(3x+6)
= 6x(x+2)+3(x+2)
=(6x+3)(x+2)
=3(2x+1)(x+2)
27. 6x2-15x+6
= (6x2-12x)-(3x-6)
= 6x(x-2)-3(x-2)
=(6x-3)(x-2)
=3(2x-1)(x-2)
28. 6x2+20x+6
= (6x2+18x)+(2x+6)
= 6x(x+3)+2(x+3)
= (6x+2)(x+3)
= 2(3x+1)(x+3)
29.6x2-20x+6
= (6x2-18x)-(2x-6)
= 6x(x-3)+2(x-3)
= (6x-2)(x-3)
= 2(3x-1)(x-3)
30.6x2+12x+6
= (6x2+6x)+(6x+6)
= 6x(x+1)+6(x+1)
= (6x+6)(x+1)
= 6(x+1)(x+1)
= 6(x+1)2
\(4a^2b^2-\left(a^2+b^2-c^2\right)^2\)
\(=4a^2b^2-2ab\left(a^2+b^2-c^2\right)+2ab\left(a^2+b^2-c^2\right)-\left(a^2+b^2-c^2\right)^2\)
\(=2ab\left[2ab-\left(a^2+b^2-c^2\right)\right]+\left(a^2+b^2-c^2\right)\left[2ab-\left(a^2+b^2-c^2\right)\right]\)
\(=\left(2ab+a^2+b^2-c^2\right)\left(2ab-a^2-b^2+c^2\right)\)
\(=\left(a^2+ab+ab+b^2-c^2\right)\left[c^2-\left(a^2-ab-ab+b^2\right)\right]\)
\(=\left[a\left(a+b\right)+b\left(a+b\right)-c^2\right]\left[c^2-\left(a\left(a-b\right)-b\left(a-b\right)\right)\right]\)
\(=\left[\left(a+b\right)^2-c^2\right]\left[c^2-\left(a-b\right)^2\right]\)
\(=\left[\left(a+b\right)^2-c\left(a+b\right)+c\left(a+b\right)-c^2\right]\left[c^2+c\left(a-b\right)-c\left(a-b\right)-\left(a-b\right)^2\right]\)
\(=\left[\left(a+b\right)\left(a+b-c\right)+c\left(a+b-c\right)\right]\left[c\left(c+a-b\right)-\left(a-b\right)\left(c+a-b\right)\right]\)
\(=\left(a+b+c\right)\left(a+b-c\right)\left(c+a-b\right)\left(c-a+b\right)\)
1.a) (3x+1)2-4(x-2)2= (3x+1)2-[2(x-2)]2=[(3x+1)-2(x-2)][(3x+1)+2(x-2)]=(x+3)(5x-1)
b) (a2+b2-5)2-4(ab+2)2= (a2+b2-5)2-[2(ab+2)]2 = (a2+b2-5-2ab-4)(a2+b2-5+2ab+4)=[(a-b)2-9][(a+b)2-1]
2. 3x2+9x-30=3x2-6x+15x-30=3x(x-2)+15(x-2)=3(x+5)(x-2)
b. x3-5x2-14x=x3+2x2-7x2-14x=x2(x+2)-7x(x+2)=(x2-7x)(x+2)
a) \(\left(3x+1\right)^2-4\left(x-2\right)^2\)
\(=\left(3x+1\right)^2-\left[2.\left(x-2\right)\right]^2\)
\(=\left(3x+1\right)^2-\left(2x-4\right)^2\)
\(=\left[3x+1-2x+4\right].\left[3x+1+2x-4\right]\)
\(=\left(x+5\right)\left(5x-3\right)\)
b) \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5\right)^2-\left[2.\left(ab+2\right)\right]^2\)
\(=\left(a^2+b^2-5\right)^2-\left(2ab+4\right)^2\)
\(=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\)
\(=\left[\left(a-b\right)^2-9\right].\left[\left(a+b\right)^2-1\right]\)
\(=\left[\left(a-b-3\right)\left(a-b+3\right)\right].\left[\left(a+b-1\right)\left(a+b+1\right)\right]\)
a) \(3x^2+9x-30\)
\(=3\left(x^2+3x-10\right)\)
\(=3\left(x^2-2x+5x-10\right)\)
\(=3.\left[x\left(x-2\right)+5.\left(x-2\right)\right]\)
\(=3.\left[\left(x+5\right)\left(x-2\right)\right]\)
b) \(x^3-5x^2-14x\)
\(=x\left(x^2-5x-14\right)\)
\(=x\left(x^2+2x-7x-14\right)\)
\(=x.\left[x\left(x+2\right)-7.\left(x+2\right)\right]\)
\(=x.\left[\left(x-7\right)\left(x+2\right)\right]\)
\(x^5+x^4+1\)
\(=x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)
\(=\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\)
\(=x^3.\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x+1\right)\)
cảm ơn bạn nhiều, không biết còn cách không? Mong nhận đượ giúp đỡ!
Giải thích: `x^2-5x+1`
`=x^2-2. 5/2x+25/4-21/4`
`=(x-5/2)^2-21/4`
`=(x-5/2-\sqrt{21}/2)(x-5/2+\sqrt{21}/2)`
`=(x-[5+\sqrt{21}]/2)(x-[5-\sqrt{21}]/2)`