(3х-4у)²-(3х-4у)(3х+4у)
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 \(-24xy + 32y^2\).
