大师作文网计算1.25(x+y)^2-16(x-y)^2
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/12 10:47:33
计算1.25(x+y)^2-16(x-y)^2
1.25(x+y)^2-16(x-y)^2
2.(a^2+b^2-1)^2-4a^2b^2
3.(a+1/2)^2乘(a^2+1/4)^2乘(a-1/2)^2
1.25(x+y)^2-16(x-y)^2
2.(a^2+b^2-1)^2-4a^2b^2
3.(a+1/2)^2乘(a^2+1/4)^2乘(a-1/2)^2
1.
25(x+y)^2 - 16(x-y)^2
= (5x+5y - 4x + 4y)(5x+5y+4x-4y)
= (x+9y)(9x+y)
2.
(a^2+b^2-1)^2 - 4a^2b^2
= (a^2 + b^2 - 1 + 2ab)(a^2 + b^2 - 1 - 2ab)
= [(a+b)^2 - 1][(a-b)^2 - 1]
= (a+b+1)(a+b-1)(a-b+1)(a-b-1)
3.
(a+1/2)^2(a^2+1/4)^2(a-1/2)^2
= (a^2+1/4)^2[(a+1/2)(a-1/2)]^2
= (a^2+1/4)^2(a^2 - 1/4)^2
= [a^4 - 1/16]^2
25(x+y)^2 - 16(x-y)^2
= (5x+5y - 4x + 4y)(5x+5y+4x-4y)
= (x+9y)(9x+y)
2.
(a^2+b^2-1)^2 - 4a^2b^2
= (a^2 + b^2 - 1 + 2ab)(a^2 + b^2 - 1 - 2ab)
= [(a+b)^2 - 1][(a-b)^2 - 1]
= (a+b+1)(a+b-1)(a-b+1)(a-b-1)
3.
(a+1/2)^2(a^2+1/4)^2(a-1/2)^2
= (a^2+1/4)^2[(a+1/2)(a-1/2)]^2
= (a^2+1/4)^2(a^2 - 1/4)^2
= [a^4 - 1/16]^2
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