1) x² + (a +b)xy + aby²
= x² + ax + by + aby²
= x( x + a) + by (1 + ay)
2) x² - (2a + b) xy + 2aby²
= x² - (2axy + bxy) + 2aby²
= x² - 2axy + bxy + 2aby²
= ( x² + bxy ) - (2axy - 2aby²)
= x (x + by) - 2ay (x + by)
= (x - 2ay) (x + by)
3) ab(x² + y²) + xy (a² + b²)
= x²ab + y²ab + a²xy + b²xy
= (x²ab + a²xy) + (y²ab + b²xy)
=ax (bx + ay) + by (ay +bx)
= (ax + by) (ay + bx)
4) xy (a² + 2b²) + ab ( 2x² + y²)
= a²xy + 2b²xy + 2x²ab + y²ab
= ( a²xy+ y²ab) + (2b²xy + 2x²ab)
= ay (ax + by) + 2bx (by + ax)
= (ay + 2bx) (ax + by)
5) (xy + ab)² + (ay - bx)²
= [(xy)² + 2.xy.ab + (ab)²] + [(ay)² - 2.ay.bx +(bx)²]
= x²y² + 2xyab + a²b² + a²y² - 2xyab + b²x²
=x²y² + a²b² + a²y² + b²x²
= (x²y² + b²x²)+ (a²b² + a²y²)
= x² (y² + b²) + a² ( b² + y²)
= ( x² + a²) ( b² + y²)
6) (xy + 4ab)² + 4(ay - bx)²
= [(xy)² + 2.xy.4ab + (4ab)²] + 4 [(ay)² - 2.ay.bx + (bx)²]
=x²y² + 8xyab + 16a²b² + 4 (a²y² -2xyab + b²x²)
=x²y² + 8xyab + 16a²b² + 4a²y² -8xyab + 4b²x²
=x²y² + ( 8xyab - 8xyab) + 16a²b² + 4a²y² + 4b²x²
= x²y² + 16a²b² + 4a²y² + 4b²x²
= ( x²y² + 4b²x²) + (16a²b² + 4a²y² )
= x² (y² + 4b²) + 4a² ( 4b² + y²)
= (x² + 4a²) ( 4b² + y²)
7) (xy - 3ab)² + (3ay + bx)²
= [(xy)² - 2.xy.3ab + (3ab)²] + [(3ay)² + 2.3ay.bx + (bx)²]
=x²y² - 6xyab + 9a²b² + 9a²y² + 6xyab + b²x²
= x²y² - ( 6xyab - 6xyab )+ 9a²b² + 9a²y² + b²x²
= x²y² + 9a²b² + 9a²y² + b²x²
= ( x²y² +b²x²) + (9a²b² + 9a²y² )
=x² (y² + b²) + 9a² ( b² + y²)
= (x² + 9a²) (b² + y²)
CHO MÌNH XIN CÂU TRA LỜI HAY NHẤT NHÁ! THANKS KIU
