Question

Упростите выражение: 1) (x^2−6y^2)(x^4+6x^2y^2+36y^4) 2) (0,2a^4−3^b)(0,04a^8+0,6a^4b+9b^2) 3) (0,4m^4−5^n)(0,16m^8+2m^4n+25n^2)

Answer 1

1)=x^6-216y^6
2)=0,008a¹²-27b³
3)=0,064m¹²-125n³

Answer 2

1) (x^2−6y^2)(x^4+6x^2y^2+36y^4)

First, let's simplify the expression by multiplying the terms using the distributive property:

(x^2)(x^4) + (x^2)(6x^2y^2) + (x^2)(36y^4) - (6y^2)(x^4) - (6y^2)(6x^2y^2) - (6y^2)(36y^4)

Simplify each term:

x^6 + 6x^4y^2 + 36x^2y^4 - 6x^4y^2 - 36x^2y^4 - 216y^6

Combine like terms:

x^6 - 6x^4y^2 - 216y^6

So, the simplified expression is:

x^6 - 6x^4y^2 - 216y^6

2) (0,2a^4−3^b)(0,04a^8+0,6a^4b+9b^2)

First, let's simplify the expression by multiplying the terms using the distributive property:

(0,2a^4)(0,04a^8) + (0,2a^4)(0,6a^4b) + (0,2a^4)(9b^2) - (3^b)(0,04a^8) - (3^b)(0,6a^4b) - (3^b)(9b^2)

Simplify each term:

0,008a^12 + 0,12a^8b + 1,8a^4b^2 - 0,12a^8b - 1,8a^4b^2 - 27b^3

Combine like terms:

0,008a^12 - 0,12a^8b - 27b^3

So, the simplified expression is:

0,008a^12 - 0,12a^8b - 27b^3

3) (0,4m^4−5^n)(0,16m^8+2m^4n+25n^2)

First, let's simplify the expression by multiplying the terms using the distributive property:

(0,4m^4)(0,16m^8) + (0,4m^4)(2m^4n) + (0,4m^4)(25n^2) - (5^n)(0,16m^8) - (5^n)(2m^4n) - (5^n)(25n^2)

Simplify each term:

0,064m^12 + 0,8m^8n + 10m^4n^2 - 0,8m^8n - 10m^4n^2 - 125n^3

Combine like terms:

0,064m^12 - 0,8m^8n - 125n^3

So, the simplified expression is:

0,064m^12 - 0,8m^8n - 125n^3