Câu 1:

\(4x^2+16x-9\)

\(=4x^2+18x-2x-9\)

\(=2x\left(2x+9\right)-\left(2x+9\right)\)

\(=\left(2x-1\right)\left(2x+9\right)\)

Câu 2:

\(6x^2-11x+3=0\)

\(\Leftrightarrow6x^2-2x-9x+3=0\)

\(\Leftrightarrow2x\left(3x-1\right)-3\left(3x-1\right)=0\)

\(\Leftrightarrow\left(2x-3\right)\left(3x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=3\\3x=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)

`9x^2+6x-8=0`

`<=> 9x^2+12x-6x-8=0`

`<=> 3x(3x+4) - 2(3x+4)=0`

`<=>(3x+4)(3x-2)=0`

`<=> 3x+4=0` hoặc `3x-2=0`

`<=> 3x=-4` hoặc `3x=2`

`<=>x=-4/3` hoặc `x=2/3`

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`2x^2 +3x-27=0`

`<=> 2x^2+9x-6x-27=0`

`<=>x(2x+9) - 3(2x+9)=0`

`<=> (2x+9)(x-3)=0`

`<=> 2x+9=0` hoặc `x-3=0`

`<=> 2x=-9` hoặc `x=3`

`<=>x=-9/2` hoặc `x=3`

\(4a^2b^2-\left(a^2+b^2-c^2\right)^2\)

\(=4a^2b^2-2ab\left(a^2+b^2-c^2\right)+2ab\left(a^2+b^2-c^2\right)-\left(a^2+b^2-c^2\right)^2\)

\(=2ab\left[2ab-\left(a^2+b^2-c^2\right)\right]+\left(a^2+b^2-c^2\right)\left[2ab-\left(a^2+b^2-c^2\right)\right]\)

\(=\left(2ab+a^2+b^2-c^2\right)\left(2ab-a^2-b^2+c^2\right)\)

\(=\left(a^2+ab+ab+b^2-c^2\right)\left[c^2-\left(a^2-ab-ab+b^2\right)\right]\)

\(=\left[a\left(a+b\right)+b\left(a+b\right)-c^2\right]\left[c^2-\left(a\left(a-b\right)-b\left(a-b\right)\right)\right]\)

\(=\left[\left(a+b\right)^2-c^2\right]\left[c^2-\left(a-b\right)^2\right]\)

\(=\left[\left(a+b\right)^2-c\left(a+b\right)+c\left(a+b\right)-c^2\right]\left[c^2+c\left(a-b\right)-c\left(a-b\right)-\left(a-b\right)^2\right]\)

\(=\left[\left(a+b\right)\left(a+b-c\right)+c\left(a+b-c\right)\right]\left[c\left(c+a-b\right)-\left(a-b\right)\left(c+a-b\right)\right]\)

\(=\left(a+b+c\right)\left(a+b-c\right)\left(c+a-b\right)\left(c-a+b\right)\)

\(4x+8+x+2\\ =4\left(x+2\right)+1.\left(x+2\right)\\ =\left(x+2\right)\left(4+1\right)\)

Đề là +8 mới phân tích được nhé!

\(\text{4x + 8x + x + 2}\)

\(\text{= (4x + 8x + x) + 2}\)

\(\text{= 13x + 2}\)

\(e,y^3+9y=y\left(y^2+9\right)\\ f,y^3-9y=y\left(y-3\right)\left(y+3\right)\\ g,xy^3+4xy^2+4xy=xy\left(y+2\right)^2\\ h,x^3-6x^2+9x=x\left(x-3\right)^2\)

\(e,3\left(x+1\right)-7\left(x-2\right)=1\\ \Leftrightarrow3x+3-7x+14=0\\ \Leftrightarrow4x=17\Leftrightarrow x=\dfrac{4}{17}\\ f,x\left(x-4\right)+9\left(4-x\right)=0\\ \Leftrightarrow\left(x-9\right)\left(x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=9\\x=4\end{matrix}\right.\\ g,x^2-8x+15=0\\ \Leftrightarrow\left(x-5\right)\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\\ h,\left(x+2\right)^2+\left(x+2\right)\left(x-5\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x+2+x-5\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)

1) x² - 4x + 3

= x² - x - 3x + 3

= (x² - x) - (3x - 3)

= x.(x - 1) - 3.(x - 1)

= (x - 1).(x - 3)

2) x² - x - 6

= x² + 2x - 3x - 6

= (x² + 2x) - (3x + 6)

= x.(x + 2) - 3.(x + 2)

= (x + 2).(x - 3)

3) x² + 5x + 4

= x² + x + 4x + x

= (x² + x) + (4x + x)

= x.(x + 1) + 4.(x + 1)

= (x + 1).(x + 4)

4) x² + 5x + 6

= x² + 2x + 3x + 6

= (x² + 2x) + (3x + 6)

= x.(x + 2) + 3.(x + 2)

= (x + 2).(x + 3)

a,=x^2+x+3x+3

=x(x+1)+3(x+1)

=(x+3)(x+1)

b,x^2-3x+2x-6

=x(x-3)+2(x-3)

=(x+2)(x-3)

2 câu còn lại từ lm nha.........

1) = x(x-3) - (x-3) = (x-3)(x-1)

làm 1) các câu khác cũng z

a. `6x(x-2015)-x+2015=6x(x-2015)-(x-2015)=(x-2015)(6x-1)`

b. `x^4+4x^2+4=(x^2)^2+2.x^2 .2 +2^2=(x^2+2)^2`

a) \(6x\left(x-2015\right)-x+2015\)

\(=6x\left(x-2015\right)-\left(x-2015\right)\)

\(=\left(x-2015\right)\left(6x-1\right)\)

b) \(x^4+4x^2+4\)

\(=x^4+2\cdot x^2\cdot2+2^2\)

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