Question

1 Выполни умножение:)(2v+u5)⋅(4v2−2vu5+u10) . 2 Разложи на множители: 8d3+c12 3 Выполни умножение (4t−3g)⋅(16t2+12tg+9g2) . 4 Разложи на множители: (d10+x10)2−(d10−x10)2−d2x2 . 5 Решить уравнение: x2+10x+16=0 . 6 Представь в виде произведения z12t24−1 . 7 Реши уравнение: (3x−2)2−(x−14)2=0 . ПОМОГИТЕ, ПОЖАЛУЙСТА, РЕШАЕТСЯ МОЯ ОЦЕНКА ЗА ЧЕТВЕРТЬ

Answer 1

1. (2v+u^5)(4v²-2vu^5+u^10)=8v³+u^15

2. 8d³+c^12=(2d+c⁴)(4d²-2dc⁴+c^8)

3. (4t-3g)(16t²+12tg+9g²)=64t³-27g³

4. (d^10+x^10)2-(d^10-x^10)2-d²x²=2d^10+2x^10-2d^10+2x^10-d²x²=4x^10-d²x²=x²(4x^8-d²)

5. x²+10x+16=0

D¹=25-16=9=3²

x¹=-5+3=-2

x²=-3-5=-8

Ответ: -2; -8.

6. z^12t^24-1=(z^6t^12-1)(z^6t^12+1)

или же (z⁴t^8-1)(z^8t^16+z⁴t^8+1)

7. (3x-2)²-(x-14)²=0

9x²-12x+4-x²+28x-196=0

8x²+16x-192=0 : 8

x²+2x-24=0

D¹=1+24=25=5²

x¹=-1+5=4

x²=-1-5=-6

Ответ: 4; -6.

Answer 2

1. Выполнение умножения: (2v+u5)⋅(4v2−2vu5+u10)

To multiply the given expression, we can use the distributive property of multiplication over addition. We multiply each term in the first expression by each term in the second expression and then combine like terms.

(2v + u5) ⋅ (4v2 - 2vu5 + u10)

= 2v ⋅ 4v2 + 2v ⋅ (-2vu5) + 2v ⋅ u10 + u5 ⋅ 4v2 + u5 ⋅ (-2vu5) + u5 ⋅ u10

Simplifying further:

= 8v3 + (-4v2u) + 2v u10 + 4v2u5 + (-2vu10) + u15

= 8v3 - 4v2u + 2vu10 + 4v2u5 - 2vu10 + u15

Therefore, the result of the multiplication is 8v3 - 4v2u + 2vu10 + 4v2u5 - 2vu10 + u15.

2. Разложение на множители: 8d3 + c12

To factorize the given expression, we need to find the common factors of the terms.

8d3 + c12

Both terms have no common factors other than 1. Therefore, the expression 8d3 + c12 cannot be factored further.

3. Выполнение умножения: (4t - 3g) ⋅ (16t2 + 12tg + 9g2)

To multiply the given expression, we can again use the distributive property of multiplication over addition. We multiply each term in the first expression by each term in the second expression and then combine like terms.

(4t - 3g) ⋅ (16t2 + 12tg + 9g2)

= 4t ⋅ 16t2 + 4t ⋅ 12tg + 4t ⋅ 9g2 - 3g ⋅ 16t2 - 3g ⋅ 12tg - 3g ⋅ 9g2

Simplifying further:

= 64t3 + 48t2g + 36tg2 - 48t2g - 36tg2 - 27g3

= 64t3 - 27g3

Therefore, the result of the multiplication is 64t3 - 27g3.

4. Разложение на множители: (d10 + x10)2 - (d10 - x10)2 - d2x2

To factorize the given expression, we can use the difference of squares formula, which states that a2 - b2 = (a + b)(a - b).

(d10 + x10)2 - (d10 - x10)2 - d2x2

= [(d10 + x10) + (d10 - x10)][(d10 + x10) - (d10 - x10)] - d2x2

Simplifying further:

= [2d10][2x10] - d2x2

= 4d10x10 - d2x2

Therefore, the factored form of the expression is 4d10x10 - d2x2.

5. Решение уравнения: x2 + 10x + 16 = 0

To solve the given equation, we can use the quadratic formula, which states that for an equation of the form ax2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b2 - 4ac)) / (2a)

For the given equation x2 + 10x + 16 = 0, we have a = 1, b = 10, and c = 16.

Using the quadratic formula:

x = (-(10) ± √((10)2 - 4(1)(16))) / (2(1))

Simplifying further:

x = (-10 ± √(100 - 64)) / 2

x = (-10 ± √36) / 2

x = (-10 ± 6) / 2

This gives us two possible solutions:

x1 = (-10 + 6) / 2 = -4 / 2 = -2

x2 = (-10 - 6) / 2 = -16 / 2 = -8

Therefore, the solutions to the equation x2 + 10x + 16 = 0 are x = -2 and x = -8.

6. Представление в виде произведения: z12t24 - 1

To represent the given expression as a product, we can use the difference of squares formula, which states that a2 - b2 = (a + b)(a - b).

z12t24 - 1

= (z6t12 + 1)(z6t12 - 1)

Therefore, the given expression z12t24 - 1 can be represented as the product (z6t12 + 1)(z6t12 - 1).

7. Решение уравнения: (3x - 2)2 - (x - 14)2 = 0

To solve the given equation, we can use the difference of squares formula, which states that a2 - b2 = (a + b)(a - b).

(3x - 2)2 - (x - 14)2 = 0

= [(3x - 2) + (x - 14)][(3x - 2) - (x - 14)] = 0

Simplifying further:

= (4x - 16)(2x + 12) = 0

Setting each factor equal to zero:

4x - 16 = 0 or 2x + 12 = 0

Solving each equation:

4x = 16 or 2x = -12

x = 4 or x = -6

Therefore, the solutions to the equation (3x - 2)2 - (x - 14)2 = 0 are x = 4 and x = -6.

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