Question

Преобразовать в многочлен стандартного вида :(2в+3а)(3а-2в)3а(а-3)-(а-4)^2

Answer 1

1)(2в+3а)(3а-2в) =6ав+9а²-4в²-6ав=9а²-4в²
2)3а(а-3)-(а-4)^2=3а²-9а-(а²-8а+16)=3а²-9а-а²+8а-16=4а²-а-16

Answer 2

Converting to Standard Form Polynomial:

To convert the given expression into standard form, we'll start by expanding the given expressions and simplifying the terms.

The given expression is: (2v + 3a)(3a - 2v) - 3a(a - 3) - (a - 4)^2

First, let's expand and simplify each part of the expression step by step.

1. Expanding (2v + 3a)(3a - 2v): - Using the distributive property, we get: 6av - 4v^2 + 9a^2 - 6av

This simplifies to: 9a^2 - 4v^2

2. Expanding - 3a(a - 3): - Using the distributive property, we get: -3a^2 + 9a

This simplifies to: 9a - 3a^2

3. Expanding - (a - 4)^2: - Using the formula for the square of a binomial, we get: -a^2 + 8a - 16

This simplifies to: -a^2 + 8a - 16

Now, combining all the simplified expressions, we get the standard form polynomial:

9a^2 - 4v^2 + 9a - 3a^2 - a^2 + 8a - 16

Simplifying further, we get:

5a^2 + 17a - 4v^2 - 16

So, the given expression in standard form is: 5a^2 + 17a - 4v^2 - 16