Rút gọn biểu thức:
a) (x + 5)(x – 5) + (x + 3)^2 – (x – 1)^2
b) (2x – 1)^2 – (x + 3)(x – 3) + (3x – 1)^2
c) (x + 2)^2 – 2(x + 2)(x – 3) + (x – 3)^2
d) (3x – 5)^2 + 2(3x – 5)(1 – 3x) + (3x – 1)^2
Rút gọn biểu thức: a) (x + 5)(x – 5) + (x + 3)^2 – (x – 1)^2 b) (2x – 1)^2 – (x + 3)(x – 3) + (3x – 1)^2 c) (x + 2)^2 – 2(x + 2)(x – 3) + (x – 3)^2 d)
By Abigail
Đáp án:
`a)x²+8x-17`
`b)12x²-10x+11`
`c)25`
`d)16`
Giải thích các bước giải:
`a)(x+5)(x-5)+(x+3)²-(x-1)²`
`=x²-25+x²+6x+9-(x²-2x+1)`
`=x²-25+x²+6x+9-x²+2x-1`
`=(x²+x²-x²)+(6x+2x)+(-25+9-1)`
`=x²+8x-17`
`b)(2x-1)²-(x+3)(x-3)+(3x-1)²`
`=4x²-4x+1-(x²-9)+9x²-6x+1`
`=4x²-4x+1-x²+9+9x²-6x+1`
`=(4x²-x²+9x²)+(-4x-6x)+(1+9+1)`
`=12x²-10x+11`
`c)(x+2)²-2(x+2)(x-3)+(x-3)²`
`=x²+4x+4+(-2x-4)(x-3)+x²-6x+9`
`=x²+4x+4-2x²+6x-4x+12+x²-6x+9`
`=(x²-2x²+x²)+(4x+6x-4x-6x)+(4+12+9)`
`=25`
`d)(3x-5)²+2(3x-5)(1-3x)+(3x-1)²`
`=9x²-30x+25+(6x-10)(1-3x)+9x²-6x+1`
`=9x²-30x+25+6x-18x²-10+30x+9x²-6x+1`
`=(9x²-18x²+9x²)+(-30x+6x+30x-6x)+(25-10+1)`
`=16`