Toán Lớp 8: Khai triển các biểu thức sau: a.(2x-3)^2 b.(3/2-x)^2 c.(2x+3y)^2 d.(a^2-2)^2 e.(2x-y+z)^2

Question

Toán Lớp 8:  Khai triển các biểu thức sau: a.(2x-3)^2 b.(3/2-x)^2 c.(2x+3y)^2 d.(a^2-2)^2 e.(2x-y+z)^2

truongankimtrong · Answer

$#Dứa$   a, (2x - 3)&sup2; = (2x)&sup2; - 2.2x.3 + 3&sup2; = 4x&sup2; - 12x + 9   b, ($ frac{3}{2}$-x)&sup2; = ($ frac{3}{2}$)&sup2; - 2.$ frac{3}{2}$.x + x&sup2; = $ frac{9}{4}$ - 3x + x&sup2;   c,  (2x + 3y)&sup2; = (2x)&sup2; - 2.2x.3y + 3y&sup2; = 4x&sup2; - 12xy + 9y&sup2;     d, (a&sup2; - 2)&sup2; = (a&sup2;)&sup2; - 2.a&sup2;.a + 2&sup2; = $a^{4}$ - 4a&sup2; + 4     e, (2x - y + z)&sup2; = [(2x - y) + z]&sup2; = (2x - y)&sup2; + 2(2x - y) . z + z&sup2; = 4x&sup2; - 4xy + y&sup2; + 4xz - 2xz + z&sup2;     * Sorry mải bu&ocirc;n qu&aacute; n&ecirc;n qu&ecirc;n khum lm b&agrave;i =v=

khanhngantoan · Answer

a)   (2x-3)^2   =  (2x)^2 - 2 . 2x . 3 + 3^2    = 4x^2 - 12x + 9   b)   (3/2 - x)^2    = (3/2)^2 - 2 . 3/2 . x + x^2    = 9/4 - 3x + x^2   c)   (2x+3y)^2    = (2x)^2 + 2 . 2x . 3y + (3y)^2    = 4x^2 + 12xy + 9y^2   d)   (a^2 - 2)^2   = (a^2)^2 - 2 . a^2 . 2 + 2^2    = a^4 - 4a^2+ 4   e)   (2x - y + z)^2    = [ (2x-y) + z]^2    = (2x-y)^2 + 2 (2x-y) . z + z^2    = [ (2x)^2 - 2 . 2x . y + y^2] + 2z (2x-y) + z^2    = 4x^2 - 4xy + y^2 + 4xz - 2yz + z^2