分解因式(5m²+3n²)²-(3m²+5n²)²

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 06:36:51
分解因式(5m²+3n²)²-(3m²+5n²)²

分解因式(5m²+3n²)²-(3m²+5n²)²
分解因式(5m²+3n²)²-(3m²+5n²)²

分解因式(5m²+3n²)²-(3m²+5n²)²
(5m²+3n²)²-(3m²+5n²)²
=(5m²+3n²+3m²+5n²)(5m²+3n²-3m²-5n²)
=(8m²+8n²)(2m²-2m²)
=16(m²+n²)(m²-m²)
=16(m²+n²)(m+n)(m-n)

(5m²+3n²)²-(3m²+5n²)²
=(5m²+3n²+3m²+5n²)(5m²+3n²-3m²-5n²)
=(8m²+8n²)(2m²-2n²)
=16(m²+n²)(m+n)(m-n)

(5m²+3n²)²-(3m²+5n²)²
=((5m²+3n²)+(3m²+5n²))((5m²+3n²)-(3m²+5n²))
=8(m²+n²)(2m²-2n²)
=16(m²+n²)(m+n)(m-n)