Вопрос от Александр ㅤ 14 апреля 2025 16:03

Question 1

(3х-4у)²-(3х-4у)(3х+4у)

Answer

Решение:

Given expression: $(3x - 4y)^2 - (3x - 4y)(3x + 4y)$

To simplify this expression, we can expand and simplify using the rules of algebra.

Expand $(3x - 4y)^2$: \begin{align*} (3x - 4y)^2 &= (3x - 4y)(3x - 4y) \ &= 3x \cdot 3x - 3x \cdot 4y - 4y \cdot 3x + 4y \cdot 4y \ &= 9x^2 - 12xy - 12xy + 16y^2 \ &= 9x^2 - 24xy + 16y^2 \end{align*}
Expand $(3x - 4y)(3x + 4y)$: \begin{align*} (3x - 4y)(3x + 4y) &= 3x \cdot 3x + 3x \cdot 4y - 4y \cdot 3x - 4y \cdot 4y \ &= 9x^2 + 12xy - 12xy - 16y^2 \ &= 9x^2 - 16y^2 \end{align*}
Substitute the expanded expressions back into the original expression: \begin{align*} (3x - 4y)^2 - (3x - 4y)(3x + 4y) &= (9x^2 - 24xy + 16y^2) - (9x^2 - 16y^2) \ &= 9x^2 - 24xy + 16y^2 - 9x^2 + 16y^2 \ &= 0x^2 - 24xy + 32y^2 \ &= -24xy + 32y^2 \end{align*}

Therefore, the simplified form of the expression $(3x - 4y)^2 - (3x - 4y)(3x + 4y)$ is $-24xy + 32y^2$.

Question 2

(3х-4у)²-(3х-4у)(3х+4у)

Answer

**Решение:** Given expression: $(3x - 4y)^2 - (3x - 4y)(3x + 4y)$ To simplify this expression, we can expand and simplify using the rules of algebra. 1. **Expand $(3x - 4y)^2$:** \begin{align*} (3x - 4y)^2 &= (3x - 4y)(3x - 4y) \\ &= 3x \cdot 3x - 3x \cdot 4y - 4y \cdot 3x + 4y \cdot 4y \\ &= 9x^2 - 12xy - 12xy + 16y^2 \\ &= 9x^2 - 24xy + 16y^2 \end{align*} 2. **Expand $(3x - 4y)(3x + 4y)$:** \begin{align*} (3x - 4y)(3x + 4y) &= 3x \cdot 3x + 3x \cdot 4y - 4y \cdot 3x - 4y \cdot 4y \\ &= 9x^2 + 12xy - 12xy - 16y^2 \\ &= 9x^2 - 16y^2 \end{align*} 3. **Substitute the expanded expressions back into the original expression:** \begin{align*} (3x - 4y)^2 - (3x - 4y)(3x + 4y) &= (9x^2 - 24xy + 16y^2) - (9x^2 - 16y^2) \\ &= 9x^2 - 24xy + 16y^2 - 9x^2 + 16y^2 \\ &= 0x^2 - 24xy + 32y^2 \\ &= -24xy + 32y^2 \end{align*} Therefore, the simplified form of the expression $(3x - 4y)^2 - (3x - 4y)(3x + 4y)$ is $-24xy + 32y^2$.

(3х-4у)²-(3х-4у)(3х+4у)

Ответ нейросети

Задай свой вопрос

Похожие вопросы 15