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\(=\left(4-a-b\right)\left(4+a-b\right)\), đằng trước là dấu trừ thì khi bỏ ngoặc phải đổi dấu chứ nhỉ :0
a: =4x^2+8x-3x-6
=4x(x+2)-3(x+2)
=(x+2)(4x-3)
b: =3(3x^2-2x-1)
=3(3x^2-3x+x-1)
=3(x-1)(3x+1)
c: =2x^2-4x+x-2
=2x(x-2)+(x-2)
=(x-2)(2x+1)
d: =3x^2+3x-2x-2
=3x(x+1)-2(x+1)
=(x+1)(3x-2)
e: =3x^2+9x+x+3
=3x(x+3)+(x+3)
=(x+3)(3x+1)
a) \(4x^2+5x-6\)
\(=4x^2+8x-3x-6\)
\(=\left(4x^2+8x\right)-\left(3x+6\right)\)
\(=4x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(4x-3\right)\)
b) \(9x^2-6x-3\)
\(=3\left(3x^2-2x-1\right)\)
\(=3\left(3x^2-3x+x-1\right)\)
\(=3\left[3x\left(x-1\right)+\left(x-1\right)\right]\)
\(=3\left(x-1\right)\left(3x+1\right)\)
c) \(2x^2-3x-2\)
\(=2x^2-4x+x-2\)
\(=\left(2x^2-4x\right)+\left(x-2\right)\)
\(=2x\left(x-2\right)+\left(x-2\right)\)
\(=\left(2x+1\right)\left(x-2\right)\)
d) \(3x^2+x-2\)
\(=3x^2+3x-2x-2\)
\(=\left(3x^2+3x\right)-\left(2x+2\right)\)
\(=3x\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-2\right)\)
e) \(3x^2+10x+3\)
\(=3x^2+9x+x+3\)
\(=3x\left(x+3\right)+\left(x+3\right)\)
\(=\left(x+3\right)\left(3x+1\right)\)
Bài 2:
1) \(x^2-4x+4=\left(x-2\right)^2\)
2) \(x^2-9=x^2-3^2=\left(x-3\right)\left(x+3\right)\)
3) \(1-8x^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)
4) \(\left(x-y\right)^2-9x^2=\left(x-y\right)^2-\left(3x\right)^2=\left(x-y-3x\right)\left(x-y+3x\right)=\left(-2x-y\right)\left(4x-y\right)\)
5) \(\dfrac{1}{25}x^2-64y^2=\left(\dfrac{1}{5}x-8y\right)\left(\dfrac{1}{5}x+8y\right)\)
6) \(8x^3-\dfrac{1}{8}=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
a)x3+3x2+3x+1
=x3+3x2*1+3x*12+13
=(x+1)3
b)(x+y)2-9x2
=y2+2xy+x2-9x2
=y2-2xy+4xy-8x2
=y(y-2x)+4x(y-2x)
=(y-2x)(y+4x)
\(9\left(x-3y\right)^2-25\left(2x+y\right)^2\)
\(=\left[3\left(x-3y\right)\right]^2-\left[5\left(2x+y\right)\right]^2\)
\(=\left(3x-9y\right)^2-\left(10x+5y\right)^2\)
\(=\left[3x-9y+10x+5y\right]\left[3x-9y-\left(10x+5y\right)\right]\)
\(=\left(13x-4y\right)\left(-7x-14y\right)\)
\(=-7\left(x+2y\right)\left(13x-4y\right)\)
9(x - 3y)² - 25(2x + y)²
= 3².(x - 3y)² - 5².(2x + y)²
= (3x - 9y)² - (10x + 5y)²
= (3x - 9y - 10x - 5y)(3x - 9y + 10x + 5y)
= (-7x - 14y)(13x - 4y)
= -7(x + 2y)(13x - 4y)
\(x^2+3x-10\)
\(=x^2+5x-2x-10\)
\(=\left(x^2+5x\right)-\left(2x+10\right)\)
\(=x\left(x+5\right)-2\left(x+5\right)\)
\(=\left(x-2\right)\left(x+5\right)\)
Thích hđt thì chiều :))
x2 + 3x - 10
= ( x2 + 3x + 9/4 ) - 49/4
= ( x + 3/2 )2 - ( 7/2 )2
= ( x + 3/2 - 7/2 )( x + 3/2 + 7/2 )
= ( x - 2 )( x + 5 )
\(27x^3-a^3b^3\)
\(=\left(3x\right)^3-\left(ab\right)^3\)
\(=\left(3x-ab\right)\left[\left(3x\right)^2+3x\cdot ab+\left(ab\right)^2\right]\)
\(=\left(3x-ab\right)\left(9x^2+3xab+a^2b^2\right)\)
\(=\left[\left(x+y\right)^3-1\right]-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left[\left(x+y\right)^2+1+2\left(x+y\right)\right]-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+y^2+2xy+1+2x+2y-3xy\right)\)
\(=\left(x+y+1\right)\left(x^2+y^2-xy+1+2x+2y\right)\)
\(=\left(x+y-1\right)\left[\left(x^2+1+2x\right)\left(y^2-xy+2y\right)\right]\)
\(=\left(x+y-1\right)\left(x+1\right)^2\left(y-x+2\right)y\)
\(a,a^2y^2+b^2x^2-2abxy\\ =\left(ay\right)^2-2abxy+\left(bx\right)^2\\ =\left(ay-bx\right)^2=\left(bx-ay\right)^2\\ ---\\ b,100-\left(3x-y\right)^2\\ =10^2-\left(3x-y\right)^2\\ =\left(10-3x+y\right)\left(10+3x-y\right)\)
a) \(=\left(ay\right)^2-2abxy+\left(bx\right)^2\)
\(=\left(ay-bx\right)^2\)
b) \(100-\left(3x-y\right)^2\)
\(=10^2-\left(3x-y\right)^2\)
\(=\left(10-3x+y\right)\left(10+3x-y\right)\)