Hướng dẫn trả lời:
Bài 1:
a) `A = (4x + 3y)cdot(4x - 3y) - 16x^2 + 10y^2 - 3xy`
`= [(4x)^2 - (3y)^2] - 16x^2 + 10y^2 - 3xy`
`= (16x^2 - 9y^2) - 16x^2 + 10y^2 - 3xy`
`= 16x^2 - 9y^2 - 16x^2 + 10y^2 - 3xy`
`= (16x^2 - 16x^2) + (- 9y^2 + 10y^2) - 3xy`
`= y^2 - 3xy`
`B = (2x + 1)^2 + (x - 1)cdot(x + 1) - (3x - 5)^2`
`= [(2x)^2 + 2cdot2xcdot1 + 1^2] + (x^2 - 1^2) - [(3x)^2 - 2cdot3xcdot5 + 5^2]`
`= (4x^2 + 4x + 1) + (x^2 - 1) - (9x^2 - 30x + 25)`
`= 4x^2 + 4x + 1 + x^2 - 1 - 9x^2 + 30x - 25`
`= (4x^2 + x^2 - 9x^2) + (4x + 30x) + (1 - 1 - 25)`
`= - 4x^2 + 34x - 25`
`C = (x - 2)cdot(x^2 + 2x + 4) - (3x + 1)^2 + (x - 2)^2`
`= (x - 2)cdot(x^2 + xcdot2 + 2^2) - [(3x)^2 + 2cdot3xcdot1 + 1^2] + (x^2 - 2cdotxcdot2 + 2^2)`
`= (x^3 - 2^3) - (9x^2 + 6x + 1) + (x^2 - 4x + 4)`
`= (x^3 - 8) - (9x^2 + 6x + 1) + (x^2 - 4x + 4)`
`= x^3 - 8 - 9x^2 - 6x - 1 + x^2 - 4x + 4`
`= x^3 + (- 9x^2 + x^2) + (- 6x - 4x) + (- 8 - 1 + 4)`
`= x^3 - 8x^2 - 10x - 5`
`D = 2xycdot(x^2 - xy + 2y^2) - (x + y)cdot(x^2 + 2xy + y^2)`
`= 2x^3y - 2x^2y^2 + 4xy^3 - (x^3 + 2x^2y + xy^2 + x^2y + 2xy^2 + y^3)`
`= 2x^3y - 2x^2y^2 + 4xy^3 - (x^3 + 3x^2y + 3xy^2 + y^3)`
`= 2x^3y - 2x^2y^2 + 4xy^3 - x^3 - 3x^2y - 3xy^2 - y^3`
Bài 2:
a) `37cdot63`
`= (50 - 13)cdot(50 + 13)`
`= 50^2 - 13^2`
`= 2500 - 169`
`= 2331`
Giải thích:
Áp dụng HĐT `A^2 - B^2 = (A + B)cdot(A - B)`
b) `599^2`
`= (600 - 1)^2`
`= 600^2 - 2cdot600cdot1 + 1^2`
`= 360000 - 1200 + 1`
`= 358801`
Giải thích:
Áp dụng HĐT `(A - B)^2 = A^2 - 2AB + B^2`
c) `1002^2`
`= (1000 + 2)^2`
`= 1000^2 + 2cdot1000cdot2 + 2^2`
`= 1000000 + 4000 + 4`
`= 1004004`
Giải thích:
Áp dụng HĐT `(A + B)^2 = A^2 + 2AB + B^2`
d) `550^2`
`= (500 + 50)^2`
`= 500^2 + 2cdot500cdot50 + 50^2`
`= 250000 + 50000 + 2500`
`= 302500`
Giải thích:
Áp dụng HĐT `(A + B)^2 = A^2 + 2AB + B^2`
