Question

Превратить в многочлен стандартного вида. 1. а) (3а^2-5) (3а^2+5) б) (3а^2-в^3) ^2 2. а) (а^2+4)(а-2)(а+2) б) (-7а-1) ^2

Answer 1

1. а) (3а²-5) (3а²+5)= 9a⁴-25.

б) (3а²-в³)²= 9a⁴-6a²в³+в⁶.

2. а) (а²+4)(а-2)(а+2)= (а²+4)(а²-4)= а⁴-16.

б) (-7а-1)²= 49а²+14а+1.

Answer 2

1) 9а^4-25
2) а^4-16
3) 9а^4-6а^2 в^3+в^6
4) 49а^2+14а+1

Answer 3

а) (3a^2 - 5)(3a^2 + 5)

To convert it to standard form, we can use the formula for multiplying two binomials: (a + b)(a - b) = a^2 - b^2.

In this case, let's treat (3a^2 - 5) as "a" and (3a^2 + 5) as "b".

Using the formula, we have: (3a^2 - 5)(3a^2 + 5) = (3a^2)^2 - 5^2 = 9a^4 - 25

Therefore, the polynomial in standard form is 9a^4 - 25.

б) (3a^2 - b^3)^2

To expand this expression, we can use the formula for squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2.

In this case, let's treat (3a^2 - b^3) as "a".

Using the formula, we have: (3a^2 - b^3)^2 = (3a^2)^2 - 2(3a^2)(b^3) + (b^3)^2 = 9a^4 - 6a^2b^3 + b^6

Therefore, the polynomial in standard form is 9a^4 - 6a^2b^3 + b^6.

а) (a^2 + 4)(a - 2)(a + 2)

To multiply these factors, we can start by expanding (a^2 + 4)(a - 2) using the distributive property:

(a^2 + 4)(a - 2) = a^3 - 2a^2 + 4a - 8

Now we can multiply this expression by (a + 2) using the distributive property again:

(a^3 - 2a^2 + 4a - 8)(a + 2) = a^4 + 2a^3 - 2a^2 - 4a^2 - 8a + 8a + 16

Combining like terms, we have: a^4 + 2a^3 - 6a^2 + 16

Therefore, the polynomial in standard form is a^4 + 2a^3 - 6a^2 + 16.

б) (-7a - 1)^2

To expand this expression, we can use the formula for squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2.

In this case, let's treat (-7a - 1) as "a".

Using the formula, we have: (-7a - 1)^2 = (-7a)^2 - 2(-7a)(1) + (1)^2 = 49a^2 + 14a + 1

Therefore, the polynomial in standard form is 49a^2 + 14a + 1.