Question

1) (a+b)^3+ (a-b)^3; 2) 3 (2 - a)^2+4 (a - 5)^2

Answer 1

Ответ:

Объяснение:

1) (a+b)³+ (a-b)³=a³+3a²b+3ab²+b³-(a³-3a²b+3ab²-b³)=

=a³+3a²b+3ab²+b³-a³+3a²b-3ab²+b³=

=2b³+6a²b

2) 3 (2 - a)²+4 (a - 5)²= 3(4-4a+a²)+4(a²-10a+25)=

=7a²-52a+112

Answer 2

Let's simplify the given expressions step by step:

1. (a+b)^3 + (a-b)^3

Expanding both terms using the binomial cube formula: (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3

Now, we can substitute these expanded forms into the expression: (a+b)^3 + (a-b)^3 = (a^3 + 3a^2b + 3ab^2 + b^3) + (a^3 - 3a^2b + 3ab^2 - b^3)

Simplifying further, we combine like terms: = a^3 + a^3 + 3a^2b - 3a^2b + 3ab^2 + 3ab^2 + b^3 - b^3 = 2a^3 + 6ab^2

Therefore, the simplified expression is 2a^3 + 6ab^2.

2. 3(2 - a)^2 + 4(a - 5)^2

Expanding both terms using the square of a binomial formula: (2 - a)^2 = (2 - a)(2 - a) = 2(2) - 2(a) - a(2) + a(a) = 4 - 4a - 2a + a^2 = 4 - 6a + a^2 (a - 5)^2 = (a - 5)(a - 5) = a(a) - 5(a) - 5(a) + 5(5) = a^2 - 5a - 5a + 25 = a^2 - 10a + 25

Now, we can substitute these expanded forms into the expression: 3(2 - a)^2 + 4(a - 5)^2 = 3(4 - 6a + a^2) + 4(a^2 - 10a + 25)

Simplifying further, we distribute the coefficients: = 12 - 18a + 3a^2 + 4a^2 - 40a + 100

Combining like terms: = 7a^2 - 58a + 112

Therefore, the simplified expression is 7a^2 - 58a + 112.