将下列各式分解因式:(1) (m+n)²+n² (2)49(a-b)²-16(a+b)
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将下列各式分解因式:(1) (m+n)²+n² (2)49(a-b)²-16(a+b)²
将下列各式分解因式:(1) (m+n)²+n² (2)49(a-b)²-16(a+b)² (3) (2x+y)²-(x+2y)² (4) (x²+y²)²-x²y² (5) 3ax²-(3ay ^4) (6) p^4-1
将下列各式分解因式:(1) (m+n)²+n² (2)49(a-b)²-16(a+b)² (3) (2x+y)²-(x+2y)² (4) (x²+y²)²-x²y² (5) 3ax²-(3ay ^4) (6) p^4-1
(1) (m+n)²-n²
=(m+n+n)(m+n-n)
=m(m+2n)
(2)49(a-b)²-16(a+b)²
=[7(a-b)+4(a+b)][7(a-b)-4(a+b)]
=(11a-3b)(3a-11b)
(3) (2x+y)²-(x+2y)²
=(2x+y+x+2y)(2x+y-x-2y)
=3(x+y)(x-y)
(4) (x²+y²)²-x²y²
=(x²+y²+xy)(x²+y²-xy)
(5) 3ax²-(3ay ^4)
=3a(x²-y^4)
=3a(x+y²)(x-y²)
(6) p^4-1
=(p²+1)(p²-1)
=(p²+1)(p+1)(p-1)
=(m+n+n)(m+n-n)
=m(m+2n)
(2)49(a-b)²-16(a+b)²
=[7(a-b)+4(a+b)][7(a-b)-4(a+b)]
=(11a-3b)(3a-11b)
(3) (2x+y)²-(x+2y)²
=(2x+y+x+2y)(2x+y-x-2y)
=3(x+y)(x-y)
(4) (x²+y²)²-x²y²
=(x²+y²+xy)(x²+y²-xy)
(5) 3ax²-(3ay ^4)
=3a(x²-y^4)
=3a(x+y²)(x-y²)
(6) p^4-1
=(p²+1)(p²-1)
=(p²+1)(p+1)(p-1)
八下数学分解因式的题(m+n)²-n² 49(a-b)²-16(a+b)² (2
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