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h) (x+1)(x+4)(x+2)(x+3) - 24
= (x2+4x+x+4)(x2+3x+2x+6)-24
=(x2+5x+5-1)(x2+5x+5+1)-24
=(x2+5x+5)2 -12 -24
=(x2+5x+5)2 -25
=(x2+5x+5)2 -52
=(x2+5x+5-5)(x2+5x+5+5)
=(x2+5x)(x2+5x+10)
i) 4(x2+5x+10x+50)(x2+6x+12x+72)-3x2
=4[x(x+5)+10(x+5)].[x(x+6)+12(x+6)]- 3x2
=4(x+10)(x+5)(x+12)(x+6)-3x2
=4(x+10)(x+6)(x+12)(x+5)-3x2
=4(x2+6x+10x+60)(x2+5x+12x+60)-3x2
=4(x2+16x+60)(x2+17x+60)-3x2
Đặt (x2+16x+60) = a
Ta có: 4a(a+x)-3x2
=4a2+4ax -3x2
=(2a)2 + 2.2a.x +x2 -4x2
= [ (2a) +x]2 - (2x)2
= [ (2a) +x -2x].[(2a) + x +2x)]
=[ (2a) -x].[(2a) + 3x)]
sau đó ta thế a = (x2+16x+60) rồi rút gọn là xong ^^
a) 3x2 - 6x
= 3x.x - 6x
= x(3x - 6)
b) 2xy + 2xyz
= 2xy(1+z)
c)15x2y - 9x2y2
= 3.5x2y - 3.3x2y.y
= 3x2y(5 - 3y)
d) 27x3 + 6x2
= 3.9x2.x + 3.2x2
= 3x2(9x +3)
e) 2x2(x-3) - x(x-3)
= (x-3)(2x2-x)
a, 15x3 - 15x = 0
15x(x2-1)=0
15x=0 hoặc x2-1=0 (tự tính nhoa)
b,3x2-6x+3=0
3(x2-2x+1)=0
x2 -2x+1=0:3=3
x2-2x=3-1=2
x(x-2)=0
x=0 hoặc x-2=0 (tự tính nhoa)
Bài làm
a) 15x3-15x=0
<=> 15x( x2 - 1 ) = 0
<=> \(\orbr{\begin{cases}15x=0\\x^2-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}}\)
Vậy x = { 0; + 1 }
b) 3x2 - 6x + 3 = 0
<=> 3( x2 - 2x + 1 ) = 0
<=> x2 - 2x + 1 = 0
<=> ( x - 1 )2 = 0
<=> x - 1 = 0
<=> x = 1
Vậy x = 1
c) 5(x - 1) - 3x(1 - x) = 0
<=> 5(x - 1) + 3x(x - 1) = 0
<=> (5 + 3x)(x - 1) = 0
<=> \(\orbr{\begin{cases}5+3x=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-\frac{5}{3}\\x=1\end{cases}}}\)
Vậy x = { -5/3; 1 }
e) -7(x + 2) = 2x(x + 2)
<=> -7(x + 2 ) - 2x( x + 2 ) = 0
<=> (x + 2)(-7 - 2x) = 0
<=> \(\orbr{\begin{cases}x+2=0\\-7-2x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-\frac{7}{2}\end{cases}}}\)
Vậy x = { -2; x = -7/2 }
f)(2x - 3)(3x + 5) = (x - 1)(3x + 5)
<=> (2x - 3)(3x + 5) - (x - 1)(3x + 5) = 0
<=> (3x + 5)(2x - 3 - x + 1) = 0
<=> (3x + 5)(x - 2) = 0
<=> \(\orbr{\begin{cases}3x+5=0\\x-2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-\frac{5}{3}\\x=2\end{cases}}}\)
Vậy x = { -5/3; 2 }
a) \(A_4=\left(x^2-3x+5\right)^2+7x\cdot\left(x^2-3x+5\right)+12x^2\)
\(=\left(x^2-3x+5\right)^2+4x\cdot\left(x^2-3x+5\right)+3x\left(x^2-3x+5\right)+12x^2\)
\(=\left(x^2-3x+5\right)\left(x^2-3x+5+4x\right)+3x\left(x^2-3x+5+4x\right)\)
\(=\left[\left(x^2-3x+5\right)+3x\right]\cdot\left(x^2-3x+5+4x\right)\)
\(=\left(x^2-3x+5+3x\right)\left(x^2+x+5\right)\)
\(=\left(x^2+5\right)\left(x^2+x+5\right)\)
\(A_5=2\left(x^2+5x-2\right)^2-7\left(x^2+5x-2\right)\left(x^3+3\right)+5\left(x^2+3\right)^2\)
Đặt \(x^2+5x-2=a;x^3+3=b\),Ta có:
\(2a^2-7ab+5b^2=2a^2-5ab-2ab+5b^2=a\left(2a-5b\right)-b\left(2a-5b\right)=\left(2a+5b\right)\left(a-b\right)\)
Thay \(x^2+5x-2=a;x^3+3=b\),ta có:
.......................
bn làm nốt nhé
a) (x3 + 8y3) : (2y + x)
= (x + 2y)(x2 - 2xy + 4y2) : (2y + x)
= x2 - 2xy + 4y2
b) (x3 + 3x2y + 3xy2 + y3) : (2x + 2y)
= (x + y)3 : 2(x + y)
= \(\dfrac{\left(x+y\right)^2}{2}\)
c) (6x5y2 - 9x4y3 + 15x3y4) : 3x3y2
= 3x3y2(2x2 - 3xy + 5y2) : 3x3y2
= 2x2 - 3xy + 5y2
e) Ta có: \(E=\left(3x+2\right)\left(3x-5\right)\left(x-1\right)\left(9x+10\right)+24x^2\)
\(=\left(9x^2-15x+6x-10\right)\left(9x^2+10x-9x-10\right)+24x^2\)
\(=\left(9x^2-10-9x\right)\left(9x^2-10+x\right)+24x^2\)
\(=\left(9x^2-10\right)^2-8x\left(9x^2-10\right)-9x^2+24x^2\)
\(=\left(9x^2-10\right)^2-8x\left(9x^2-10\right)+15x^2\)
\(=\left(9x^2-10\right)^2-3x\left(9x^2-10\right)-5x\left(9x^2-10\right)+15x^2\)
\(=\left(9x^2-10\right)\left(9x^2-3x-10\right)-5x\left(9x^2-10-3x\right)\)
\(=\left(9x^2-3x-10\right)\left(9x^2-5x-10\right)\)