七下完全平方公式计算题

Question

1、49²-38*49+19²
2、【（x-2y）（x+2y）】²+【（x-2y）²-（x+2y）²】²

Answer 1

原式=49²-2×19×49+19²
=(49-19)²
=30²
=900

原式=(x-2y)²+2(x-2y)(x+2y)+(x+2y)²+(x-2y)²-2(x-2y)(x+2y)+(x+2y)²
=2(x-2y)²+2(x+2y)²
=2x²-8xy+8y²+2x²+8xy+8y²
=4x²+16y²本回答被提问者采纳

Answer 2

49²-38*49+19²

= 49²-2*19*49+19²

= (49-19)²
= 30²
= 900

[(x-2y)(x+2y)]² +[(x-2y)² -(x+2y)²]²

= [x²-4y²]² +[x²-4xy+4y² -x²-4xy-4y²]²
= [x⁴-8x²y²+16y⁴] +16x²y²
= x⁴+8x²y²+16y⁴
= (x²+4y²)²

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Answer 3

1、49²-38*49+19²=(49-19)^2=900
2、【（x-2y）-（x+2y）】²+【（x-2y）²-（x+2y）²】²
=16y^2+[(x-2y+x+2y)(x-2y-2x-2y)]^2
=16y^2+64x^4y^4