Question

运用乘法公式计算

1. (x+1)^2(x-1)^2
2. [(a+b)^2+(a-b)^2]^2
3. 已知xy=9,x-y=-3,求x^2+3xy+y^2

Answer 1

1. (x+1)^2(x-1)^2
=[(x+1)(x-1)]^2
=(x^2-1)^2
=x^4-2x^2+1;

2. [(a+b)^2+(a-b)^2]^2
=(2a^2+2b^2)^2
=4a^4+8a^2b^2+4b^4;

3. x^2+y^2=(x-y)^2+2xy=(-3)^2+2*9=27,
x^2+3xy+y^2
=(x^2+y^2)+3xy
=27+3*9
=54.

Answer 2

1. (x+1)^2(x-1)^2
=[)x+1)(x-1)]^2
=(x^2-1)^2
=x^4-2x^2+1

2. [(a+b)^2+(a-b)^2]^2
=(a^2+b^2+2ab+a^2+b^2-2ab)^2
=(2a^2+2b^2)^2
=4a^4+8a^2b^2+4b^2

3. xy=9,x-y=-3,
(x-y)^2=x^2-2xy+y^2=(-3)^2=9
x^2+y^2=9+2xy=27

x^2+3xy+y^2
=(x^2+y^2)+3xy
=27+27
=54