数学习题

展开(x+1)²

• x² + 2

• x² + 1

• x² + 2x - 1

• x² + 2x + 1

Answer explanation

To expand (x+1)^2, we use the formula (a+b)^2 = a^2 + 2ab + b^2. In this case, a=x and b=1. Therefore, (x+1)^2 = x^2 + 2x + 1, which matches the option x^2 + 2x + 1.

展开（x+3)(3x-5)

• 3x²+14x-15

• 3x²-14x-15

• 3x²+4x-15

• 3x²-4x-15

Answer explanation

To expand (x+3)(3x-5), use the distributive property. First, multiply x by 3x and x by -5 to get 3x^2-5x. Then, multiply 3 by 3x and 3 by -5 to get 9x-15. Combine like terms to get 3x^2+9x-5x-15 = 3x^2+4x-15.

已知8^a=5, 4^b=6, 求2^3a+2b

• 32

• 30

• 24

• 无解

Answer explanation

To find 2^(3a+2b), we substitute the given values: 8^a = 5 -> 2^(3a) = 5, 4^b = 6 -> 2^(2b) = 6. Therefore, 2^(3a+2b) = 2^(3a) * 2^(2b) = 5 * 6 = 30. Hence, the correct answer is 30.

展开(x+y)(x-y)(x²+y²)(x⁴+y⁴)(x⁸+y⁸)

• x³⁰ - y³⁰

• x¹⁶ - y¹⁶

• x¹⁵ - y¹⁵

• x¹⁴ - y¹⁴

Answer explanation

To expand the given expression, we can use the difference of squares formula multiple times. After simplifying, we get x^16 - y^16 as the result.

1+2+3+4+5+6+....+997+998+999+1000=?

• 500500

• 50000

• 55000

• 50500

Answer explanation

The sum of the first n natural numbers is given by the formula n*(n+1)/2. Here, n=1000. So, the sum is 1000*1001/2 = 500500. Therefore, the correct answer is 500500.

因式分解x²-3x+2

• (x+2)(x-1)

• (x+1)(x-2)
• (x-1)(x+1)
• (x-1)(x-2)

因式分解x¹²⁸-y¹²⁸

• (x⁶⁴ + y⁶⁴)(x³² + y³²)(x⁸ + y⁸)(x⁴ + y⁴)(x²+ y²)(x + y)(x - y)

• (x⁶⁴ + y⁶⁴)(x¹⁶ + y¹⁶)(x⁸ + y⁸)(x⁴ + y⁴)(x² + y²)(x + y)(x - y)

• (x⁶⁴ + y⁶⁴)(x³²+ y³²)(x¹⁶ + y¹⁶)(x⁸ + y⁸)(x⁴ + y⁴)(x² + y²)(x + y)(x - y)

• (x³² + y³²)(x¹⁶ + y¹⁶)(x⁸ + y⁸)(x⁴ + y⁴)(x² + y²)(x + y)(x - y)

Answer explanation

The correct choice is (x^64 + y^64)(x^32+ y^32)(x^16 + y^16)(x^8 + y^8)(x^4 + y^4)(x^2 + y^2)(x + y)(x - y) as it correctly factors x^128 - y^128.

求x²+4x+4, 2x+4和3x+6的最高公因式 (HCF)

• 2x - 4
• x + 4
• x + 2
• x - 2

求x⁴-y⁴, x²+2xy+y²和2x+2y的最低公倍式 (LCM)

• 2(x+y)²(x-y)(x²+y²)

• 2(x+y)(x²+y²)

• x+y

• 2(x+y)(x²+y²)

求64的平方根