Question

1.173^2-174*172 2.12345^2-12346*12344 3.（x+3)(x-1)-x(x+4) 4.(2m-3n)(m+4n)-(m+n)(2m+5n)

5.(3x-4y)(-3x-4y)-(-2x-y)(-2x+y) 6.(1/3a+3/2b)(1/3a-3/2b) 7.(2a+1)^2-(2a-1)^2 8.-3x(x+1)(x-1)-x(3x+2)(2-3x) 9.-4(2y-1/2)(1/2+2y)+3(2x-3)(2x+1) 10.(a+2)(a-2)-a(a+1) 11.(x+1/3)(x^2+1/9)(x-1/3) 12.(2^2+1)(2^4+1)(2^8+1)(2^16+1)

Answer 1

1.173^2-174*172
=173²-(173+1)(173-1)
=173²-173²+1
=1

2.12345^2-12346*12344
=12345²-(12345+1)(12345-1)
=12345²-12345²+1
=1

3.（x+3)(x-1)-x(x+4)
=x²+2x-3-x²-4x
=-2x-3

4.(2m-3n)(m+4n)-(m+n)(2m+5n)
=2m²+5mn-12n²-2m²-7mn-5n²
=-2mn-17n²

5.(3x-4y)(-3x-4y)-(-2x-y)(-2x+y)
=-9x²+16y²-4x²+y²
=-13x²+17y²

6.(1/3a+3/2b)(1/3a-3/2b)
=1/9a²-9/4b²

7.(2a+1)^2-(2a-1)^2
=4a²+4a+1-4a²+4a-1
=8a

8.-3x(x+1)(x-1)-x(3x+2)(2-3x)
=-3x³+3x-4x+9x³
=6x³-x

9.-4(2y-1/2)(1/2+2y)+3(2x-3)(2x+1)
=1-16y²+12x²-12x-9
=12x²-12x-16y²-8

10.(a+2)(a-2)-a(a+1)
=a²-4-a²-a
=-a-4

11.(x+1/3)(x^2+1/9)(x-1/3)
=(x²-1/9)(x²+1/9)
=x^4-1/81

12.(2^2+1)(2^4+1)(2^8+1)(2^16+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)÷(2+1)
=(2²-1)(2²+1)(2^4+1)(2^8+1)(2^16+1)÷3
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)÷3
=(2^8-1)(2^8+1)(2^16+1)÷3
=(2^16-1)(2^16+1)÷3
=(2^32-1)÷3