5m^2 + 30mn -90n^2 = квадрат суммы квадрат разности

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вопрос

To find out if the given expression is the square of the sum or the square of the difference, we can compare it to the formulas for each.

The square of the sum of two terms, (a + b)^2, is equal to a^2 + 2ab + b^2.

The square of the difference of two terms, (a - b)^2, is equal to a^2 - 2ab + b^2.

Given expression: 5m^2 + 30mn - 90n^2

To make it easier to compare, let's rewrite the given expression as:

5m^2 + 30mn - 90n^2 = ( )^2

Now we need to determine the values that make the given expression equal to the square of a binomial. Let's try to match the given expression with the perfect square trinomial formulas.

The coefficient of the middle term in both formulas is 2. Therefore, we need to divide the coefficient of the middle term in the given expression by 2 and square that result.

30mn / 2 = 15mn

(15mn)^2 = 225m^2n^2

Let's rewrite the given expression with this middle term:

5m^2 + 30mn - 90n^2 = 5m^2 + 30mn + 225m^2n^2 - 315m^2n^2 - 90n^2

Now we can see that the middle term 30mn can be expressed as 2ab where a = m and b = 15n.

(5m + 15n)^2

Therefore, 5m^2 + 30mn - 90n^2 is the square of the sum of 5m and 15n, which is (5m + 15n)^2.