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Bài 1:
a: \(x^2\left(3x+2\right)=3x^3+2x^2\)
b: \(\left(x-2\right)\left(3x^2-4x+1\right)\)
\(=3x^3-4x^2+x-6x^2+8x-2\)
\(=3x^2-10x^2+9x-2\)
c: \(\left(3x+2\right)\left(9x^2-6x+4\right)-\left(x-3\right)\left(x+3\right)\)
\(=27x^3+8-x^2+9=27x^3-x^2+17\)
d: \(=\left(x+y-x-y+z\right)\left(x+y+x+y-z\right)\)
\(=z\left(2x+2y-z\right)\)
\(=2xz+2yz-z^2\)
a) x2-y2-5x+5y=(x2-y2)-(5x-5y)
=(x-y)(x+y)-5(x-y)
=(x-y)(x+y-5)
b) 16x2-(x+y)2=(4x)2-(x+y)2
=(4x-x-y)(4x+x+y)
=(3x-y)(5x+y)
c) 5x2+6xy+y2=5x2+5xy+xy+y2
=5x(x+y)+y(x+y)
=(x+y)(5x+y)
d) a2-2a+2b-b2=( a2-b2)-(2a-2b)
= (a-b)(a+b)-2(a-b)
=(a-b)(a+b-2)
a) x2 - y2 - 5x + 5y
= (x2 - y2) - (5x - 5y)
= (x - y)(x + y) - 5(x - y)
= (x - y)(x + y - 5)
b) 16x2 - (x + y)2
= (4x)2 - (x + y)2
= (4x - x - y)(4x + x + y)
= (3x - y)(5x + y)
c) 5x2 + 6xy + y2
= 5x2 + 5xy + xy + y2
= 5x(x + y) + y(x + y)
= (x + y)(5x + y)
d) a2 - 2a + 2b - b2
= (a2 - b2) - (2a - 2b)
= (a - b)(a + b) - 2(a - b)
= (a - b)(a + b - 2)
a) x2 + 4x – y2 + 4;
=x2+4x+4-y2
=(x+2)2-y2
=(x+2-y)(x+2+y)
b) 3x2 + 6xy + 3y2 – 3z2;
=3.(x2+2xy+y2)-3z2
=3.(x+y)2-3z2
=3.[(x+y)2-z2]
=3.(x+y-x)(x+y+z)
c) x2 – 2xy + y2 – z2 + 2zt – t2.
=(x-y)2-(z2-2zt+t2)
=(x-y)2-(z-t)2
=[(x-y)-(z-t)][(x-y)+(z-t)]
=(x-y-z+t)(x-y+z-t)
a) bt \(=\left(x-8\right)\left(x^2-x-2\right)=\left(x-8\right)\left(x+1\right)\left(x-2\right)\)
kl: ...
b) \(=\left(x+2\right)\left(x^2-8x-15\right)=\left(x+2\right)\left(x-5\right)\left(x-3\right)\)
kl:....
a, \(x^3-9x^2+6x+16\)
\(=x^3-8x^2-x^2+8x-2x+16\)
\(=x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\)
\(=\left(x-8\right)\left(x^2-x-2\right)\)
\(=\left(x-8\right)\left(x^2-2x+x-2\right)\)
\(=\left(x-8\right)\left[x\left(x-2\right)+\left(x-2\right)\right]\)
\(=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)
b, \(x^3-6x^2-x+30\)
\(=x^3-5x^2-x^2+5x-6x+30\)
\(=x^2\left(x-5\right)-x\left(x-5\right)-6\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2-x-6\right)\)
\(=\left(x-5\right)\left(x^2-3x+2x-6\right)\)
\(=\left(x-5\right)\left[x\left(x-3\right)+2\left(x-3\right)\right]\)
\(=\left(x-5\right)\left(x-3\right)\left(x+2\right)\)
Chúc bạn học tốt!!!
a)\(x^2+4x-4y^2-8y\)
\(=x^2+2xy+4x-2xy-4y^2-8y\)
\(=x\left(x+2y+4\right)-2y\left(x+2y+4\right)\)
\(=\left(x-2y\right)\left(x+2y+4\right)\)
b)sai đề
c)sai đề tiếp
a)x2+4x-4y2-8y=(x2-4y2)+(4x-8y)
=(x+2y(x-2y)+4(x-2y)
=(x-2y)(x+2y+4)
a)3y(x2 -2xy+y)
b)=(a+b)(a-b)+2(a+b)
=(a+b)(a-b+2)
b)
c)
d)
c)=(x+3)2-y2
=(x+3+y)(x+3-y)
d) x2 - 9x + 20
=x2-4x-5x+20
=x(x-4)-5(x+4)
=x(x-4)-5(x-4)
=(x-4)(x-5)
a) 3x2y-6xy2+3y2
= 3y(x2-2xy+3y)
b) a2-b2+2a+2b
= (a+b)(a-b)+2(a+b)
= (a+b)(a-b+2)
c) x2+6x+9-y2
= (x+3)2-y2
= (x+3-y)(x+3+y)
d) x2-9x+20
= x2-4x-5x+20
= x(x-4)-5(x-4)
= (x-5)(x-4)