Question

1)Разложи на множители 25y2+10y+1 2)Выполни умножение:(6c4−7d2)⋅(6c4+7d2) Выбери правильный ответ Заранее спасибо за ответ

Answer 1

1) (5y - 1)(5y + 1); 2)36c^8 - 49d^4

Answer 2

Factoring 25y^2 + 10y + 1

To factor the expression 25y^2 + 10y + 1, we can use the quadratic formula or look for common factors. In this case, there are no common factors, so we will use the quadratic formula.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the expression 25y^2 + 10y + 1, the coefficients are: a = 25, b = 10, and c = 1.

Plugging these values into the quadratic formula, we get:

y = (-10 ± √(10^2 - 4 * 25 * 1)) / (2 * 25)

Simplifying further:

y = (-10 ± √(100 - 100)) / 50

y = (-10 ± √0) / 50

Since the discriminant (b^2 - 4ac) is zero, the quadratic equation has a single real root. Therefore, the expression 25y^2 + 10y + 1 cannot be factored further.

Multiplying (6c^4 - 7d^2) * (6c^4 + 7d^2)

To multiply the expressions (6c^4 - 7d^2) and (6c^4 + 7d^2), we can use the distributive property.

The distributive property states that for any real numbers a, b, and c:

a * (b + c) = a * b + a * c

Applying this property to the given expressions, we have:

(6c^4 - 7d^2) * (6c^4 + 7d^2) = 6c^4 * 6c^4 + 6c^4 * 7d^2 - 7d^2 * 6c^4 - 7d^2 * 7d^2

Simplifying further:

= 36c^8 + 42c^4d^2 - 42c^4d^2 - 49d^4

Combining like terms, we get:

= 36c^8 - 49d^4

Therefore, the product of (6c^4 - 7d^2) and (6c^4 + 7d^2) is 36c^8 - 49d^4.

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