Question

Замените звездочки такими одночленами,чтобы образовалось тождество:1) (*+6b)^2=*+24ab+* 2) (*-*)^2=9m^4-42m^2n^8+* Помогите пожалуйста, срочно

Answer 1

1) (2а+6b)^2 = 4a^2 +24ab +36b^2

Answer 2

Task: Replace the asterisks with monomials to form an identity:

1) (* 6b)^2 = * 24ab + 2) (* - *)^2 = 9m^4 - 42m^2n^8 + *

To solve this task, we need to find the missing monomials that will make the given expressions true. Let's solve each equation separately:

1) (* 6b)^2 = * 24ab +

To find the missing monomials, we can expand the expression on the left side of the equation using the exponent rule for multiplication:

(* 6b)^2 = (6b)^2 = 36b^2

Now, let's compare the expanded expression with the right side of the equation:

36b^2 = * 24ab +

To make this equation true, we need to find the missing monomial that, when added to 24ab, will give us 36b^2. The missing monomial is 12b^2:

36b^2 = 24ab + 12b^2

Therefore, the missing monomial is 12b^2.

2) (* - *)^2 = 9m^4 - 42m^2n^8 + *

To find the missing monomial, we can expand the expression on the left side of the equation using the exponent rule for multiplication:

(* - *)^2 = (-)^2 = 1

Now, let's compare the expanded expression with the right side of the equation:

1 = 9m^4 - 42m^2n^8 + *

To make this equation true, we need to find the missing monomial that, when added to 9m^4 - 42m^2n^8, will give us 1. The missing monomial is -9m^4 + 42m^2n^8:

1 = 9m^4 - 42m^2n^8 + (-9m^4 + 42m^2n^8)

Therefore, the missing monomial is -9m^4 + 42m^2n^8.

To summarize, the missing monomials are: 1) 12b^2 2) -9m^4 + 42m^2n^8

I hope this helps! Let me know if you have any further questions.