Toán Lớp 8: 1/ x ² -2x+1-y ² 2/ x ²-2xy+y ²- 9z ² 3/ x ²-4xy +4y ²-z ²+4zt -4t ² 4/ a^4 -ax ³ -ay+xy 5/ x ² +2x+1-y ² 6/ x ² + 2xy +y ²- 4z ² 7/ x

Question

Toán Lớp 8:  1/ x ² -2x+1-y ² 2/ x ²-2xy+y ²- 9z ² 3/ x ²-4xy +4y ²-z ²+4zt -4t ² 4/ a^4 -ax ³ -ay+xy 5/ x ² +2x+1-y ² 6/ x ² + 2xy +y ²- 4z ² 7/ x ²-2xy +y ² -z ² +2zt - t ² 8/ a ³ -ax ² -ay +xy

minhtuquynh · Answer

1. x^2-2x+1-y^2   = (x-1)^2-y^2   = (x-1-y)(x-1+y)   2. x^2-2xy+y^2-9z^2   = (x-y)^2-9z^2   = (x-y-3z)(z-y+3z)   3. x^2-4xy+4y^2-z^2+4zt-4t^2   = (x^2-4xy+4y^2)-(z^2-4zt+4t^2)   = (x-2y)^2-(z-2t)^2   = (x-2y-z+2t)(x-2y+z-2t)   4. a^4-ax^3-ay+xy   = x(a^3-x^3)-y(a-x)   = x(a-x)(a^2+ax+x^2)-y(a-x)   = x(a-x)(a^2+ax+x^2-y)   5. x^2+2xy+1-y^2   = (x+1)^2-y^2   = (x+1-y)(x+1+y)   6. x^2+2xy+y^2-4z^2   = (x+y)^2-4z^2   = (x+y-2z)(z+y+2z)   7. x^2-2xy+y^2-z^2+2zt-t^2   = (x^2-2xy+y^2)-(z^2-2zt+t^2)   = (x-y)^2-(z-t)^2   = (x-y-z+t)(x-y+z-t)   8. a^3-ax^2-ay+xy   = a(a^2-x^2)-y(a-x)   = a(a-x)(a+x)+y(a-x)   = a(a-x)(a+x+y)

thaolanphuobg · Answer

Giải đáp+Lời giải và giải thích chi tiết:    1, x&sup2; - 2x + 1 - y&sup2;   = (x - 1)&sup2; - y&sup2;   =(x - 1 - y ).(x - 1 + y)   2, x&sup2; - 2xy + y&sup2; - 9z&sup2;   = (x - y)&sup2; - 9z&sup2;   = (x - y - 3z).(x - y + 3z)   3, x&sup2; - 4xy + 4y&sup2; - z&sup2; + 4zt - 4t&sup2;   = (x&sup2; - 4xy + 4y&sup2;) - (z&sup2; - 4zt + 4t&sup2;)   =( x - 2y)&sup2; - (z - 2t)&sup2;   = (x - 2y - z + 2t).(x - 2y + z - 2t)   4, $a^{4}$ - ax&sup3; - ay + xy   = a(a&sup3; - x&sup3;) - (ay - xy)   = a.(a- x).(a&sup2; + ax +x&sup2;) - y(a - x)   = (a - x).(a&sup3; + a&sup2;x + ax&sup2; - y)   5, x&sup2; + 2x + 1 - y&sup2;   = (x + 1)&sup2; - y&sup2;   = (x + 1 - y).(x + 1 + y)   6, x&sup2; + 2xy + y&sup2; - 4z&sup2;   =(x + y )&sup2; - 4z&sup2;   = (x + y - 2z).(x + y + 2z)   7, x&sup2; - 2xy + y&sup2; - z&sup2; + 2zt - t&sup2;   = (x&sup2; - 2xy + y&sup2;) - (z&sup2; - 2zt + t&sup2;)   = (x - y)&sup2; - (z - t)&sup2;   = (x - y + z - t).(x - y - z  + t)   8, a&sup3; - ax&sup2; - ay + xy   = (a&sup3; - ax&sup2; ) - (ay - xy)   = a(a&sup2; - x&sup2;) - y(a - x)   = a(a - x).(a + x) - y(a - x)   =(a - x).(a&sup2; + ax - y)