1. (3x + 5)2 =
(3x)2 +
2 . 3x . 5 + 52 =
32 . x2
+ 2 . 3x . 5 + 52 =
9x2 + 2
. 3x . 5 + 25 =
9x2 +
30x + 25
R// 9x2
+ 30x + 25
2. (x2 - 2)3 =
(x2)3
- (3x2) 2 . 2 + (3x2) . 22 -23
=
X6 - 3x4
. 2 + 3x2 . 4 - 8 =
X6 - 6x4
+ 3x2 . 4 - 8 =
X6 - 6x4
+ 12x2 - 8
R// X6 -
6x4 + 12x2 - 8
3. (2x
- √y) (2x + √y) =
(2x)2 -
(√y)2 =
4x2 - (√y)2 =
4x2 - y
R// 4x2
- y
4. (√h2
+ 1 + 1)(√h2 + 1 − 1) =
(√h2 + 1)2
- 1 =
h2 + 1 -
1 =
h2
R// h2
5. (√a + 1/b) (√a - 1/b)=
(√a)2 - (1/b)2
=
(√a)2 - 1/b2
=
a - 1/b2
R// a - 1/b2
6. (5s - t2) =
(5s)2
- 2 . 5s . t + t2 =
52 . s2
- 2 . 5s . t + t2 =
25s2 -
10s . t + t2 =
25s2 -
10st + t2
R// 25s2
- 10st + t2
7. (1 - 2y)3 =
1 - 3 . 2y + 3(2y)2
- (2y)3 =
1 - 6y + 3(2y)2 - (2y)3 =
1 - 6y + 3 . 22 . y2 - 23 . y3
=
1 - 6y + 3 . 4y2 - 8y3 =
1 - 6y + 12y2 - 8y3
R// 1 - 6y + 12y2 - 8y3
8. (3a - b2) (9a2
+ 3ab2 + b4) =
(3a)3 - (b2)3 =
33 . a3 - (b2)3 =
27ª3 - (b2)3 =
27ª3 - b6
R// 27ª3 - b6
9. (5x + y2) (25x2
- 5xy2 + y4) =
(5x)3 + (y2)3 =
53 . x3 + (y2)3 =
125x3 + (y2)3 =
125x2 + y6
R// 125x2 + y6
10. (1 + 1/x)2 - (1 -
1/x)2 =
1 + 2 . 1/x + (1/x)2 - (1 - 2 . 1/x +(1/x)2) =
1 + 2/x + (1/x)2 - (1 - 2/x + (1/x)2) =
1 + 2/X + 1/x2 - (1 - 2/x + 1/x2) =
1 + 2/x + 1/x2 - 1 + 2/x - 1/x2 =
X2 + 2x + 1 - x2 + 2x - 1 / x2 =
4x/x2 =
4/x
R// 4/x
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