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七年级数学解答题一般
题目
化简求值:4x2−xy−(43y2+2x2)−2(3xy−13y2)4x^2-xy-(\frac{4}{3}y^2+2x^2)-2(3xy-\frac{1}{3}y^2),其中x=−1x=-1,y=12y=\frac{1}{2}.
知识点：整式、整式化简求值章节：第4章 整式的加减 / 4.1 整式

答案与解析

答案

4x2−xy−(43y2+2x2)−2(3xy−13y2)4x^2-xy-(\frac{4}{3}y^2+2x^2)-2(3xy-\frac{1}{3}y^2)
=4x2−xy−43y2−2x2−6xy+23y2=4x^{2}-xy-\frac{4}{3}y^{2}-2x^{2}-6xy+\frac{2}{3}y^{2}
=2x2−7xy−23y2=2x^{2}-7xy-\frac{2}{3}y^{2}，
当x=−1x=-1，y=12y=\frac{1}{2}时，原式=2×(−1)2−7×(−1)×12−23×(12)2=2×1+72−23×14=2+72−16=163=2\times \left(-1\right)^{2}-7\times \left(-1\right)\times \frac{1}{2}-\frac{2}{3}\times (\frac{1}{2})^{2}=2\times 1+\frac{7}{2}-\frac{2}{3}\times \frac{1}{4}=2+\frac{7}{2}-\frac{1}{6}=\frac{16}{3}.

解析

4x2−xy−(43y2+2x2)−2(3xy−13y2)4x^2-xy-(\frac{4}{3}y^2+2x^2)-2(3xy-\frac{1}{3}y^2)
=4x2−xy−43y2−2x2−6xy+23y2=4x^{2}-xy-\frac{4}{3}y^{2}-2x^{2}-6xy+\frac{2}{3}y^{2}
=2x2−7xy−23y2=2x^{2}-7xy-\frac{2}{3}y^{2}，
当x=−1x=-1，y=12y=\frac{1}{2}时，原式=2×(−1)2−7×(−1)×12−23×(12)2=2×1+72−23×14=2+72−16=163=2\times \left(-1\right)^{2}-7\times \left(-1\right)\times \frac{1}{2}-\frac{2}{3}\times (\frac{1}{2})^{2}=2\times 1+\frac{7}{2}-\frac{2}{3}\times \frac{1}{4}=2+\frac{7}{2}-\frac{1}{6}=\frac{16}{3}.

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