4(2p+3q)^2-9(3p-q)^2 因式分解

问题描述:

4(2p+3q)^2-9(3p-q)^2 因式分解

原式=[2(2p+3q)² -(3p+q)²]
=[2(2p+3q)+3p+q][2(2p+3q)-3p-q]
=(4p+6q+3q+p)(4p+6-3q-p)
=(5p+9q)(3p+3q)
=3(5p+9q)(p+q)

4(2p+3q)^2-9(3p-q)^2
=(4p+6q-9p+3q)(4p+6q+9p-3q)
=(9q-5p)(10p+3q)

4(2p+3q)^2 - 9(3p-q)^2
=[2(2p+3q) + 3(3p-q)][2(2p+3q) - 3(3p-q)]
=(4p+6q+9p-3q)(4p+6q-9p+3q)
=(13p+3q)(9q-5p)