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

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1. 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)

   Trả lời
2. Giải đáp+Lời giải và giải thích chi tiết:

    1, x² – 2x + 1 – y²

   = (x – 1)² – y²

   =(x – 1 – y ).(x – 1 + y)

   2, x² – 2xy + y² – 9z²

   = (x – y)² – 9z²

   = (x – y – 3z).(x – y + 3z)

   3, x² – 4xy + 4y² – z² + 4zt – 4t²

   = (x² – 4xy + 4y²) – (z² – 4zt + 4t²)

   =( x – 2y)² – (z – 2t)²

   = (x – 2y – z + 2t).(x – 2y + z – 2t)

   4, $a^{4}$ – ax³ – ay + xy

   = a(a³ – x³) – (ay – xy)

   = a.(a- x).(a² + ax +x²) – y(a – x)

   = (a – x).(a³ + a²x + ax² – y)

   5, x² + 2x + 1 – y²

   = (x + 1)² – y²

   = (x + 1 – y).(x + 1 + y)

   6, x² + 2xy + y² – 4z²

   =(x + y )² – 4z²

   = (x + y – 2z).(x + y + 2z)

   7, x² – 2xy + y² – z² + 2zt – t²

   = (x² – 2xy + y²) – (z² – 2zt + t²)

   = (x – y)² – (z – t)²

   = (x – y + z – t).(x – y – z  + t)

   8, a³ – ax² – ay + xy

   = (a³ – ax² ) – (ay – xy)

   = a(a² – x²) – y(a – x)

   = a(a – x).(a + x) – y(a – x)

   =(a – x).(a² + ax – y)

   Trả lời