Hướng dẫn trả lời:
8) `15cdot(x + 5)^3 - 15xcdot(x^2 + 10)`
`= 15cdot(x^3 + 3cdotx^2cdot5 + 3cdotxcdot5^2 + 5^3) - 15xcdot(x^2 + 10)`
`= 15cdot(x^3 + 15x^2 + 75x + 125) - 15xcdot(x^2 + 10)`
`= 15x^3 + 225x^2 + 1125x + 1875 - 15x^3 - 150x`
`= 225x^2 + 975x + 1875`
9) `xcdot(x - 14) - 10cdot(x - 1)^2`
`= xcdot(x - 14) - 10cdot(x^2 - 2cdotxcdot1 + 1^2)`
`= xcdot(x - 14) - 10cdot(x^2 - 2x + 1)`
`= x^2 - 14x - 10x^2 + 20x - 10`
`= (x^2 - 10x^2) + (- 14x + 20x) - 10`
`= -9x^2 + 6x - 10`
10) `(x + 3)cdot(x - 4) - (x + 4)^2`
`= (x^2 - 4x + 3x - 12) - (x^2 + 2cdotxcdot4 + 4^2)`
`= (x^2 - x - 12) - (x^2 + 8x + 16)`
`= x^2 - x - 12 - x^2 - 8x - 16`
`= (x^2 - x^2) + (- x - 8x) + (- 12 - 16)`
`= - 9x - 28`
11) `2xcdot(x - 2) - (x + 2)cdot(x - 2)`
`= 2xcdot(x - 2) - (x^2 - 2^2)`
`= 2xcdot(x - 2) - (x^2 - 4)`
`= 2x^2 - 4x - x^2 + 4`
`= (2x^2 - x^2) - 4x + 4`
`= x^2 - 4x + 4`
12) `(2x - 3)^2 - (1 + 2x)cdot(2x - 1) + 3cdot(2x - 3)`
`= [(2x)^2 - 2cdot2xcdot3 + 3^2] - (2x + 1)cdot(2x - 1) + 3cdot(2x - 3)`
`= (4x^2 - 12x + 9) - [(2x)^2 - 1^2] + 3cdot(2x - 3)`
`= (4x^2 - 12x + 9) - (4x^2 - 1) + 3cdot(2x - 3)`
`= 4x^2 - 12x + 9 - 4x^2 + 1 + 6x - 9`
`= (4x^2 - 4x^2) + (- 12x + 6x) + (9 + 1 - 9)`
`= - 6x + 1`
13) `(x + y - 1)^2 - 2cdot(x + y - 1)cdot(x + y) + (x + y)^2`
`= [(x + y - 1) - (x + y)]^2`
`= (x + y - 1 - x - y)^2`
`= [(x - x) + (y - y) - 1]^2`
`= (-1)^2`
`= 1`
Giải thích:
Áp dụng HĐT `(A + B)^2 = A^2 + 2AB + B^2`
14) `(x + 1)^2 + (x - 1)^2 - (x - 1)cdot(x + 1)`
`= (x^2 + 2cdotxcdot1 + 1^2) + (x^2 - 2cdotxcdot1 + 1^2) - (x^2 - 1^2)`
`= (x^2 + 2x + 1) + (x^2 - 2x + 1) - (x^2 - 1)`
`= x^2 + 2x + 1 + x^2 - 2x + 1 - x^2 + 1`
`= (x^2 + x^2 - x^2) + (2x - 2x) + (1 + 1 + 1)`
`= x^2 + 3`
15) `(2x + 1)^2 + (x - 3)^2 - 2cdot(2x + 1)cdot(x - 3)`
`= (2x + 1)^2 - 2cdot(2x + 1)cdot(x - 3) + (x - 3)^2`
`= [(2x + 1) - (x - 3)]^2`
`= (2x + 1 - x + 3)^2`
`= [(2x - x) + (1 + 3)]^2`
`= (x + 4)^2`
`= x^2 + 2cdotxcdot4 + 4^2`
`= x^2 + 8x + 16`
Giải thích:
Áp dụng HĐT `(A - B)^2 = A^2 - 2AB + B^2`
16) `(2x + 1)^2 - (3 + 2x)cdot(2x - 3) - 4cdot(x + 2)`
`= [(2x)^2 + 2cdot2xcdot1 + 1^2] - (2x + 3)cdot(2x - 3) - 4cdot(x + 2)`
`= (4x^2 + 4x + 1) - [(2x)^2 - 3^2] - 4cdot(x + 2)`
`= (4x^2 + 4x + 1) - (4x^2 - 9) - 4cdot(x + 2)`
`= 4x^2 + 4x + 1 - 4x^2 + 9 - 4x - 8`
`= (4x^2 - 4x^2) + (4x - 4x) + (1 + 9 - 8)`
`= 2`
17) `(x + 2)cdot(x - 2) - 2xcdot(x + 3) + (x - 2)^2`
`= (x^2 - 2^2) - 2xcdot(x + 3) + (x^2 - 2cdotxcdot2 + 2^2)`
`= (x^2 - 4) - 2xcdot(x + 3) + (x^2 - 4x + 4)`
`= x^2 - 4 - 2x^2 - 6x + x^2 - 4x + 4`
`= (x^2 - 2x^2 + x^2) + (- 6x - 4x) + (- 4 + 4)`
`= -10x`
18) `(x - 3)^2 - (x - 2)cdot(x + 2)`
`= (x^2 - 2cdotxcdot3 + 3^2) - (x^2 - 2^2)`
`= (x^2 - 6x + 9) - (x^2 - 4)`
`= x^2 - 6x + 9 - x^2 + 4`
`= (x^2 - x^2) - 6x + (9 + 4)`
`= - 6x + 13`
