Factorisation
练习14.3
(e)' 5pq(p²- q²)÷ 2p (p + q) '
答:' 5pq(p²- q²)÷ 2p (p + q) '
使用' (a +b) (a - b) = a^2 - b^2 ';方程可以写成:
' = 5pq (p + q) (p - q) ÷ 2p (p + q) '
' = 5q(p - q) ÷ 2 '
(f)12xy (9x^2 - 16y^2) ÷ 4xy (3x + 4y) '
答:12xy (9x^2 - 16y^2) ÷ 4xy (3x + 4y) '
这可以像前面的问题一样解决;
' = 3 (3x + 4y) (3x - 4y) ÷ (3x + 4y) '
' = 3 (3x - 4y) '
(g)39y^3(50y^2 - 98) ÷ 26y^2 (5y + 7) '
答:39y^3(50y^2 - 98) ÷ 26y^2 (5y + 7) '
' = 2xx 39y^3(25y^2 - 49) ÷ 26y^2 (5y + 7) '
' = 3y (25y^2 - 49) ÷ (5y + 7) '
' = 3y (5y + 7) (5y - 7) ÷ (5y + 7) '
' = 3y (5y - 7) '
练习14.4
找出并改正下列数学语句中的错误:
问题1:' 4(x - 5) = 4x - 5 '
答:' 4(x - 5) = 4x - 20 '
问题2:' x(3x + 2) = 3x^2 + 2 '
答:' = 3x²+ 2x '
问题3:“2x + 3y = 5xy”
答:2x + 3y
在这里;X和y就像粉笔和奶酪一样不同，因此不能加在一起。
问题4:“x + 2x + 3x = 5x”
答:= 6 x
这就像加一个苹果，两个苹果和三个苹果。
问题5:“5y + 2y + y - 7y = 0”
答:' = y '
问题6:“3x + 2x = 5x^2”
答:' = 5 x '
问题7:' (2x)²+ 4(2x) + 7 = 2x²+ 8x + 7 '
答:' = 4x^2 + 8x + 7 '
问题8:' (2x)^2 + 5x = 4x + 5x = 9x '
答:4x^2 + 5x
问题9:' (3x + 2)^2 = 3x^2 + 6x + 4 '
答:使用' (a + b)^2 = a^2 + 2ab + b^2 ';
' = 9x^2 + 12x + 4 '
问题10:把x = - 3代入
(一)“x ^ 2 + 5 + 4”给“(3)^ 2 + 5 (- 3)+ 4 = 9 + 2 + 4 = 15 '
答:' = (-3)^2 + 5(-3) + 4 '
' = 9 - 15 + 4 = - 2 '
(b)“x ^ 2 - 5 x + 4”给“(3)^ 2 - 5 (- 3)+ 4 = 9 - 15 + 4 = - 2 '
答:' (- 3)^2 - 5 (- 3) + 4 '
' = 9 + 15 + 4 = 28 '
(c)“x ^ 2 + 5 x”给“(3)^ 2 + 6(3)= - 9 - 15 = - 24的
答:'(- 3)²+ 5 (- 3)'
' = 9 - 15 = - 6 '
问题11:' (y - 3)^2 = y^2 - 9 '
答:' = y²- 6y + 9 '
问题12:' (z + 5)²= z²+ 25 '
答:' = z²+ 10z + 25 '
问题13:' (2a + 3b) (a - b) = 2a^2 - 3b^2 '
答:' = 2a²- 2ab + 3ab - 3b²'
' = 2a^2 + ab - 3b^2 '
问题14:' (a + 4)(a + 2) = a^2 + 8 '
答:' = a^2 + 2a + 4a + 8 = a^2 + 6a + 8 '
问题15:' (a - 4)(a - 2) = a^2 - 8 '
答:' a^2 - 2a - 4a + 8 '
' = a^2 - 6a + 8 '
问题16:“3x^2 ÷ 3x^2 = 0”
答:= 1
问题17:' (3x^2 + 1) ÷ 3x^2 = 1 + 1 = 2 '
答:' = 1 + (1)/(3x^2) '
问题18:“3x ÷ (3x + 2) =½”
答:' = 3x ÷ (3x + 2) '
问题19:“3 ÷ (4x + 3) = 1/4x”
答:' = 3 ÷ (4x + 3) '
问题20:' (4x + 5) ÷4x = 5 '
答:' = 1 + (5)/(4x) '
问题21:“(7x + 5) ÷ 5 = 7x”
答:' = (7x)/(5) + 1 '