因式分解p²(p+a)²-q²(p-q)²打错了 应该是p²(p+q)²-q²(p-q)²
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/28 05:37:19
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因式分解p²(p+a)²-q²(p-q)²打错了 应该是p²(p+q)²-q²(p-q)²
因式分解p²(p+a)²-q²(p-q)²
打错了 应该是p²(p+q)²-q²(p-q)²
因式分解p²(p+a)²-q²(p-q)²打错了 应该是p²(p+q)²-q²(p-q)²
应用平方差公式a²-b²=(a-b)(a+b)
∴p²(p+q)²-q²(p-q)²
=[p(p+q)-q(p-q)]×[p(p+q)+q(p-q)]
=(p²+pq-pq+q²)(p²+pq+pq-q²)
=(p²+q²)(p²+2pq-q²)
p²(p+q)²-q²(p-q)²
=﹙p(p+q)﹚²-﹙q(p-q)﹚²
=﹙p(p+q)+q(p-q)﹚﹙p(p+q)-q(p-q)﹚
=﹙p²+pq+pq-q²﹚﹙p²+pq-pq+q²﹚
=﹙p²+2pq-q²﹚﹙p²+q²﹚