Question

Помогите ребят вот: 6 . Разложите на множители: а) 100a^4- одна девятая b^2 b) 9x^2-(x-1)^2 и 7.Докажите что при любых значениях Х выражение принимает положительные значения : х ВО ВТОРОЙ СТЕПЕНИ - 10 + 29 ПОМОГИИИТЕ

Answer 1

6a) $100 a^{4} - \frac{1}{9} b^{2}=(10a^{2}-\frac{1}{3} b)(10a^{2}+\frac{1}{3} b)$

6b)$9x^{2}-(x-1)^{2}=(3x-x+1)(3x+x-1)=(2x+1)(4x-1)$

7)  $x^{2}-10+29=x^{2}+19$
Квадрат любого числа = неотрицательное число
Неотрицательное число + положительное (19) = положительное значение

Answer 2

Factoring Expressions:

a) To factor the expression 100a^4 - (1/9)b^2, we can start by factoring out the greatest common factor (GCF) from both terms. The GCF of 100a^4 and (1/9)b^2 is 1/9. Factoring out 1/9, we get:

(1/9)(100a^4 - b^2)

Next, we can notice that the expression inside the parentheses is a difference of squares. The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b). Applying this formula, we have:

(1/9)(10a^2 + b)(10a^2 - b)

Therefore, the expression 100a^4 - (1/9)b^2 can be factored as (1/9)(10a^2 + b)(10a^2 - b).

b) To factor the expression 9x^2 - (x - 1)^2, we can start by expanding the square term (x - 1)^2. Using the formula (a - b)^2 = a^2 - 2ab + b^2, we have:

9x^2 - (x - 1)^2 = 9x^2 - (x^2 - 2x + 1)

Next, we can simplify the expression by distributing the negative sign:

9x^2 - (x^2 - 2x + 1) = 9x^2 - x^2 + 2x - 1

Combining like terms, we get:

9x^2 - x