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\(A=3a^2c^2+bd+3abc+acd=\left(3a^2c^2+3abc\right)+\left(bd+acd\right)=3ac\left(ac+b\right)+d\left(b+ac\right)\\ =\left(3ac+d\right)\left(ac+b\right)\)
\(B=a^2c-a^2d-b^2d+b^2c=a^2\left(c-d\right)-b^2\left(c-d\right)=\left(a^2-b^2\right)\left(c-d\right)\\=\left(a-b\right)\left(a+b\right)\left(c-d\right)\)
\(C=8x^2+4xy-2ax-ay=\left(8x^2+4xy\right)-\left(2ax+ay\right)=4x\left(2x+y\right)-a\left(2x+y\right)\\ =\left(4x-a\right)\left(2x+y\right)\)
\(E=3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2\right)-12c^2=3\left(a-b\right)^2-12c^2\\ =3\left[\left(a-b\right)^2-4c^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)
\(a, 4x^2-4y^2\)
\(= (4x-4y)(4x+4y)\)
\(b. x^2-xy+2x-2y\)
\(= (x^2-xy)+(2x-2y)\)
\(=x(x-y)+2(x-y)\)
\(=(x+2)(x-y)\)
\(c, 6x^2-7x+2\)
\(= 6x^2-4x-3x+2\)
\(=(6x^2-4x)-(3x-2)\)
\(= 2x(3x-2)-(3x-2)\)
\(=(3x-2)(2x-1)\)
phần a Sai rồi bạn nhá mik sửa cho:
\(a.4x^2-4y^2\\ =4\left(x^2-y^2\right)\\ =4\left(x-y\right)\left(x+y\right)\)
Bạn nên cẩn thận hơn ở những lần sau :))
\(3a^2c^2+bd+3abc+acd\)
\(=\left(3a^2c^2+3abc\right)+\left(acd+bd\right)\)
\(=3ac\left(ac+b\right)+d\left(ac+b\right)\)
\(=\left(ac+b\right)\left(3ac+d\right)\)
a) Áp dụng HĐT 1 thu được ( 2 x + y ) 2 .
b) Áp dụng HĐT 3 với A = 2x + l; B = x - l thu được
[(2x +1) + (x -1)] [(2x +1) - (x -1)] rút gọn thành 3x(x + 2).
c) Ta có: 9 - 6x + x 2 - y 2 = ( 3 - x ) 2 - y 2 = (3 - x - y)(3 -x + y).
d) Ta có: -(x + 2) + 3( x 2 - 4) = -{x + 2) + 3(x + 2)(x - 2)
= (x + 2) [-1 + 3(x - 2)] = (x + 2)(3x - 7).
a) \(=\left(x+6y\right)\left(x-6y\right)-\left(x-6y\right)\)
\(=\left(x-6y\right)\left(x-6y-1\right)\)
b) \(=x\left(x^2-8x+16\right)\)
\(=x\left(x-4\right)^2\)
c) \(=2\left(x-y\right)^2-18\)
\(=2\left[\left(x-y\right)^2-3^2\right]\)
\(=2\left(x-y+3\right)\left(x-y-3\right)\)
a: \(x^2-36y^2-x+6y\)
\(=\left(x-6y\right)\left(x+6y\right)-\left(x-6y\right)\)
\(=\left(x-6y\right)\left(x+6y-1\right)\)
b: \(x^3-8x^2+16x\)
\(=x\left(x^2-8x+16\right)\)
\(=x\left(x-4\right)^2\)
c: \(2x^2-4xy+2y^2-18\)
\(=2\left(x^2-2xy+y^2-9\right)\)
\(=2\left(x-y-3\right)\left(x-y+3\right)\)
d: \(3x^2-7x-10\)
\(=3x^2+3x-10x-10\)
\(=3x\left(x+1\right)-10\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-10\right)\)
a) 25 - x2 + 4xy - 4y2 = 25 - (x2 - 4xy + 4y2) = 52 - (x - 2y)2 = (5 + x - 2y)(5 - x +2y) = (x - 2y + 5)(2y - x + 5)
b) 3a2c2 + bd + 3abc + acd = (3a2c2 + 3abc) + (bd + acd) = 3ac(ac + b) + d (ac + b) = (ac + b)(3ac + d)
c) x3 - 2x2 - x + 2 = x2(x - 2) - (x - 2) = (x - 2)(x2 - 1) = (x - 2)(x - 1)(x + 1)
d) a4 + 5a3 + 15a - 9 = (a4 + 3a2) + (5a3 + 15a) - (3a2 + 9) = a2(a2 + 3) + 5a(a2 + 3) - 3(a2 + 3) = (a2 + 3)(a2 + 5a - 3)
4x^2=28x+49