谁能帮我讲一下这些因式分解的题
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:2024/11/06 17:38:27
谁能帮我讲一下这些因式分解的题
1:x^2-9(x+y)^2
2:64(a-b)^2-49(a+b)^2
3:4(3a+2b)^2-(2a+3b)^2
4:X^4-16y^4
我不太明白这些~
1:x^2-9(x+y)^2
2:64(a-b)^2-49(a+b)^2
3:4(3a+2b)^2-(2a+3b)^2
4:X^4-16y^4
我不太明白这些~
平方差公式:a^2-b^2=(a+b)(a-b)
可以把右边展开来证明,即(a+b)(a-b)=a^2-ab+ab-b^2=a^2-b^2
你这几道题都是用这个公式来做:
1.x^2-9(x+y)^2
=x^2-[3(x+y)]^2
=[x+3(x+y)][x-3(x+y)]
=(4x+3y)(-2x-3y)
=-(2x+3y)(4x+3y)
2.64(a-b)^2-49(a+b)^2
=[8(a-b)]^2-[7(a+b)]^2
=(8a-8b+7a+7b)(8a-8b-7a-7b)
=(15a-b)(a-15b)
3.4(3a+2b)^2-(2a+3b)^2
=[2(3a+2b)]^2-(2a+3b)^2
=(6a+4b+2a+3b)(6a+4b-2a-3b)
=(8a+7b)(4a+b)
4.x^4-16y^4
=(x^2)^2-(4y^2)^2
=(x^2+4y^2)(x^2-4y^2)
=(x^2+4y^2)[x^2-(2y)^2]
==(x^2+4y^2)(x+2y)(x-2y)
可以把右边展开来证明,即(a+b)(a-b)=a^2-ab+ab-b^2=a^2-b^2
你这几道题都是用这个公式来做:
1.x^2-9(x+y)^2
=x^2-[3(x+y)]^2
=[x+3(x+y)][x-3(x+y)]
=(4x+3y)(-2x-3y)
=-(2x+3y)(4x+3y)
2.64(a-b)^2-49(a+b)^2
=[8(a-b)]^2-[7(a+b)]^2
=(8a-8b+7a+7b)(8a-8b-7a-7b)
=(15a-b)(a-15b)
3.4(3a+2b)^2-(2a+3b)^2
=[2(3a+2b)]^2-(2a+3b)^2
=(6a+4b+2a+3b)(6a+4b-2a-3b)
=(8a+7b)(4a+b)
4.x^4-16y^4
=(x^2)^2-(4y^2)^2
=(x^2+4y^2)(x^2-4y^2)
=(x^2+4y^2)[x^2-(2y)^2]
==(x^2+4y^2)(x+2y)(x-2y)