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(x2 + 2.x.3 + 32 - 1).(x2 + 2.x.4 + 16 - 1) - 24
=[(x+3)2 - 1]. [(x+4)2-1] -24
=(x+3+1)(x+3-1)(x+4+1)(x+4-1) - 24
=(x+4)(x+2)(x+5)(x-3) - 24
(x2+6x+8)(x2+8x+15)-24
<=>(x2+4x+2x+8)(x2+5x+3x+15)-24
<=> [x(x+4)+2(x+4)][x(x+5)+3(x+5)]-24
<=> (x+4)(x+2)(x+5)(x+3)-24
<=> (x+4)(x+3)(x+2)(x+5)-24
<=>(x2+7x+12)(x2+7x+10)
đặt t=x2+7x+11 ta có:
(t-1)(t+1)-24
<=> t2-1-24
<=>t2-25
<=>(t-5)(t+5)
thay t=x2+7x+11 vào ta có:
(x2+7x+11-5)(x2+7x+11+5)
<=>(x2+7x+6)(x2+7x+16)
\(a,x^2+6x+9\)
\(=\left(x+3\right)^2\)
\(b,10x-25-x^2\)
\(=-\left(x^2-10x+25\right)\)
\(=-\left(x-5\right)^2\)
\(c,8x^3-\frac{1}{8}\)
\(=8x^3-\left(\frac{1}{2}\right)^3\)
\(=\left(8x-\frac{1}{2}\right)\left(64x^2+4x+\frac{1}{4}\right)\)
\(d,8x^3+12x^2+6xy^2+y^3\)
\(=2\left(4x^3+6x^2+3xy^2+\frac{1}{2}y^3\right)\)
hok tốt!
c)\(x^3-x^2+x+3=x^2+x-2x^2-2x+3x+3\)
\(=x\left(x+1\right)-2x\left(x+1\right)+3\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-2x+3\right)\)
d)\(x^8+3x^4+4=\left(x^8+4x^4+4\right)-x^4=\left(x^4+2\right)^2-\left(x^2\right)^2\)
\(=\left(x^4-x^2+2\right)\left(x^4+x^2+2\right)\)
e)\(x^6-x^4-2x^3+2x^2=x^4\left(x^2-1\right)-2x^2\left(x-1\right)=x^4\left(x-1\right)\left(x+1\right)-2x^2\left(x-1\right)\)
\(=x^2\left(x-1\right)\left(x^3+x^2\right)-2x^2\left(x-1\right)=x^2\left(x-1\right)\left(x^3+x^2-2\right)\)
\(=x^2\left(x-1\right)\left[\left(x^3-1\right)+\left(x^2-1\right)\right]=x^2\left(x-1\right)\left[\left(x-1\right)\left(x^2+x+1\right)+\left(x-1\right)\left(x+1\right)\right]\)
\(=x^2\left(x-1\right)\left(x-1\right)\left(x^2+2x+2\right)=x^2\left(x-1\right)^2\left(x^2+2x+2\right)\)
a)\(x^2-x-12\)
\(=x^2+4x-3x-12\)
\(=x\left(x+4\right)-3\left(x+4\right)\)
\(=\left(x+4\right)\left(x-3\right)\)
b) \(x^2+8x+15\)
\(=x^2+3x+5x+15\)
\(=x\left(x+3\right)+5\left(x+3\right)\)
\(=\left(x+3\right)\left(x+5\right)\)