ln hong 發問於 科學及數學數學 · 1 十年前

20fun! 幫幫手!

2(x2 + y2)(x + y)2 − (x2 − y2)2

(3a + b)(3a − b) − (a + 5b)(b − 3a)

(x2 + y2)2 − 4x2y2

4(2x − y)(3x − y) − 4(y − 2x)(x + 3y)

− 49m3yz3 + 14x2y2z2 − 21my3z

m(ab + bc + ac) − mbc

p2(p + q)2 − q2(p − q)2

2 個解答

• 1 十年前
最愛解答

1. 2(x^2 + y^2)(x + y)^2 − (x^2 − y^2)^2

= 2(x^2 + y^2)(x + y)^2 − [(x+y)(x− y)]^2

= 2(x^2 + y^2)(x + y)^2 − (x+y)^2(x− y)^2

= (x+y)^2 [2(x^2 + y^2)− (x− y)^2 ]

= (x+y)^2 [2x^2 + 2y^2− (x^2− 2xy +y^2) ]

= (x+y)^2 [x^2 + 2xy +y^2 ]

= (x+y)^2 [(x+y)^2]

= (x+y)^4

2. (3a + b)(3a − b) − (a + 5b)(b − 3a)

= (3a + b)(3a − b) + (a + 5b)(3a - b)

= (3a - b) [(3a + b) + (a + 5b)]

= (3a-b)(4a+6b)

= 2(3a-b)(2a+3b)

3. (x2 + y2)^2 − 4x^2 y^2

= x^4 + 2x^2 y^2 + y^4 - 4x^2 y^2

= x^4 - 2x^2 y^2 + y^4

= (x^2 - y^2) ^2

4. 4(2x − y)(3x − y) − 4(y − 2x)(x + 3y)

= 4(2x − y)(3x − y) + 4(2x − y)(x + 3y)

= 4(2x-y) [(3x-y)+(x+3y)]

= 4(2x-y)(4x+2y)

= 8(2x-y)(2x+y)

5. − 49m3yz3 + 14x2y2z2 − 21my3z

= (-7)myz(7m^2z^2 - 2myz +3 y^2)

6. m(ab + bc + ac) − mbc

= m(ab+bc+ac-bc)

=m(ab+ac)

=ma(b+c)

7. p2(p + q)2 − q2(p − q)2

= p^2[p^2+2pq+q^2] - q^2 [p^2-2pq+q^2]

= p^4 +2p^3q + p^2 q^2 - p^2 q^2 +2pq^3 - q^4

= p^4 +2p^3q +2pq^3 - q^4

= p^4 - q^4 +2p^3q +2pq^3

= (p^2 + q^2)(p^2 - q^2) + 2pq (q^2+p^2)

= (p^2 + q^2) ( p^2 - q^2 + 2pq)