Question

Помогите пожалуйста! Представьте в виде многочлена:1)(10m^3+0.9n^2 )*(10m^3−0.9n^2 )2)(a^2+0,2b^3)*(a^2-0,2b^3)3)(m^3+0,5)*(m^3-0,5)4)(2a+4b)*(2a-4b)5)(0,4a^2+9b)*(0,4a^2-9b)6)(5x*4+0,7y^3)*(5x-0,7y^3)Разложите на множители:1)16x^8-81y^22)0,01x^8-0,04y^4Возведение в степень:1)(-5n^4y^6)^32)(-0,5x^6 d^15)^23)(-0,2b^4 n^10)^34)(6c^2 x^4)^35)(9x^10 d^3)^46)(-0,8m^11 b^8)^27)(-9y^12 a^10)^48)(-0,4d^4 y^10)^29)(-4m^13 b^7)^310)(-7b^15 y^3)^411)(-0,2d^4 n^12)^212)(-2m^15 c^8)^413)(0,1n^3 c^7)^414)(6a^5 x^13)^4

Answer 1

1.
1) 100m^6-0.81n⁴
2) a⁴- 0.04b^6
3) m^6-0.25
4) 4a²-16b²
5) 0.16a⁴-81b²
6) 100x²-10,5xy³-0,49y^6
2.
1) 16x^8-81y²= (4x⁴-9y)•(4x⁴+9y)
2) 0.01x^8-0.04y⁴=0.01(x⁴-2y²)•(x⁴+2y²)

Answer 2

Разложение многочленов на множители:

1) (10m^3 + 0.9n^2) * (10m^3 - 0.9n^2)

To factorize this expression, we notice that it is in the form of a difference of squares. The equation can be rewritten as:

(10m^3)^2 - (0.9n^2)^2

Using the formula for the difference of squares, we can factorize this expression as:

(10m^3 + 0.9n^2) * (10m^3 - 0.9n^2)

2) (a^2 + 0.2b^3) * (a^2 - 0.2b^3)

This expression is also in the form of a difference of squares. We can factorize it as:

(a^2)^2 - (0.2b^3)^2

Using the difference of squares formula, the expression can be factored as:

(a^2 + 0.2b^3) * (a^2 - 0.2b^3)

3) (m^3 + 0.5) * (m^3 - 0.5)

This expression is not a difference of squares, so we cannot factorize it further.

4) (2a + 4b) * (2a - 4b)

This expression is also in the form of a difference of squares. We can factorize it as:

(2a)^2 - (4b)^2

Using the difference of squares formula, the expression can be factored as:

(2a + 4b) * (2a - 4b)

5) (0.4a^2 + 9b) * (0.4a^2 - 9b)

This expression is not a difference of squares, so we cannot factorize it further.

6) (5x * 4 + 0.7y^3) * (5x - 0.7y^3)

This expression is not a difference of squares, so we cannot factorize it further.

Возведение в степень:

1) (-5n^4y^6)^3

To raise this expression to the power of 3, we raise each term inside the parentheses to the power of 3:

(-5n^4y^6)^3 = -5^3 * (n^4)^3 * (y^6)^3

Simplifying each term, we have:

-5^3 = -125 (n^4)^3 = n^(4*3) = n^12 (y^6)^3 = y^(6*3) = y^18

Putting it all together, we have:

(-5n^4y^6)^3 = -125n^12y^18

2) (-0.5x^6 + d^15)^2

To raise this expression to the power of 2, we raise each term inside the parentheses to the power of 2:

(-0.5x^6 + d^15)^2 = (-0.5x^6)^2 + (d^15)^2 + 2*(-0.5x^6)*(d^15)

Simplifying each term, we have:

(-0.5x^6)^2 = (-0.5)^2 * (x^6)^2 = 0.25x^12 (d^15)^2 = (d^15)^2 = d^30 2*(-0.5x^6)*(d^15) = -x^6*d^15

Putting it all together, we have:

(-0.5x^6 + d^15)^2 = 0.25x^12 + d^30 - x^6*d^15

3) (-0.2b^4 + n^10)^3

To raise this expression to the power of 3, we raise each term inside the parentheses to the power of 3:

(-0.2b^4 + n^10)^3 = (-0.2b^4)^3 + (n^10)^3 + 3*(-0.2b^4)*(n^10)

Simplifying each term, we have:

(-0.2b^4)^3 = (-0.2)^3 * (b^4)^3 = -0.008b^12 (n^10)^3 = (n^10)^3 = n^30 3*(-0.2b^4)*(n^10) = -0.6b^4*n^10

Putting it all together, we have:

(-0.2b^4 + n^10)^3 = -0.008b^12 + n^30 - 0.6b^4*n^10

4) (6c^2 + x^4)^3

To raise this expression to the power of 3, we raise each term inside the parentheses to the power of 3:

(6c^2 + x^4)^3 = (6c^2)^3 + (x^4)^3 + 3*(6c^2)*(x^4)

Simplifying each term, we have:

(6c^2)^3 = (6)^3 * (c^2)^3 = 216c^6 (x^4)^3 = (x^4)^3 = x^12 3*(6c^2)*(x^4) = 18c^2*x^4

Putting it all together, we have:

(6c^2 + x^4)^3 = 216c^6 + x^12 + 18c^2*x^4

5) (9x^10 + d^3)^4

To raise this expression to the power of 4, we raise each term inside the parentheses to the power of 4:

(9x^10 + d^3)^4 = (9x^10)^4 + (d^3)^4 + 4*(9x^10)*(d^3)

Simplifying each term, we have:

(9x^10)^4 = (9)^4 * (x^10)^4 = 6561x^40 (d^3)^4 = (d^3)^4 = d^12 4*(9x^10)*(d^3) = 36x^10*d^3

Putting it all together, we have:

(9x^10 + d^3)^4 = 6561x^40 + d^12 + 36x^10*d^3

6) (-0.8m^11 + b^8)^2

To raise this expression to the power of 2, we raise each term inside the parentheses to the power of 2:

(-0.8m^11 + b^8)^2