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chắc bn nảy hỏi lun cả bài tâp về nhà quá, làm km 1 câu
a) = a+a+a + a +a +1 -a -a -a = a(a+a+1) +(a+a+1) - a(a+a+1)= (a+a+1)(a-a+1)
tự bn thêm mũ 4;3;2 vào được là bn làm dc cac câu sau
a: Sửa đề: x^3-x^2+5x-5
=x^2(x-1)+5(x-1)
=(x-1)(x^2+5)
b: x^3+4x^2+x-6
=x^3-x^2+5x^2-5x+6x-6
=(x-1)(x^2+5x+6)
=(x-1)(x+2)(x+3)
c: \(=\left(x+2\right)^3+y^3\)
\(=\left(x+2+y\right)\left(x^2+4x+4-xy-2y+y^2\right)\)
\(1.x^3+2x+x^2=x\left(x^2+x+2\right)\)
\(2.2x^3+4x^2+2x=2x\left(x^2+2x+1\right)=2x\left(x+1\right)^2\)
\(3.-3x^3-5x^2+8x=-3x^3+3x^2-8x^2+8x\)
\(=-3x^2\left(x-1\right)-8x\left(x-1\right)=\left(3x^2+8x\right)\left(1-x\right)\)
\(=x\left(3x+8\right)\left(1-x\right)\)
\(4.x^2+4x-5=x^2-x+5x-5=\left(x-1\right)\left(x+5\right)\)
\(5.6x^2-3x-3=6x^2-6x+3x-3=3\left(x-1\right)\left(2x+1\right)\)
\(6.3x^2-2x-5=3x^2+3x-5x-5=\left(x+1\right)\left(3x-5\right)\)
\(8.x^2-2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)\(=\left(x+2y\right)\left(x-y-2\right)\)
\(9.x^3+2x^2y+xy^2-9x=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left(x+y-3\right)\left(x+y+3\right)\)
\(10.x^2-y^2+6x+9=\left(x+3-y\right)\left(x+3+y\right)\)
Bài 1:
a)\(5x^2y^3-25x^3y^4+10x^3y^3=5x^2y^3\left(1-5xy+2x\right)\)
b)\(x^3-2xy-x^2y+2y^2=\left(x^3-x^2y\right)-\left(2xy-2y^2\right)=x^2\left(x-y\right)-2y\left(x-y\right)=\left(x-y\right)\left(x^2-2y\right)\)
c)Đề sai hoàn toàn
d) \(2x^2+4xy+2y^2-8z^2=2\left(x^2+2xy+y^2-4z^2\right)=2\left[\left(x+y\right)^2-\left(2z\right)^2\right]=2\left(x+y-2z\right)\left(x+y+2z\right)\)e) \(3x-3a+yx-ya=3\left(x-a\right)+y\left(x-a\right)=\left(x-a\right)\left(3+y\right)\)
f)\(\left(x^2+y^2\right)^2-4x^2y^2=\left(x-y\right)^2\left(x+y\right)^2\)
g)\(2x^2-5x+2=2x^2-x-4x+2=x\left(2x-1\right)-2\left(2x-1\right)=\left(2x-1\right)\left(x-2\right)\)
i)\(14x\left(x-y\right)-21y\left(y-x\right)+28z\left(x-y\right)=14x\left(x-y\right)+21y\left(x-y\right)+28z\left(x-y\right)=7\left(x-y\right)\left(2x+3y+4z\right)\)
Đặt \(x^2+3x+1=t\)
\(\left(x^2+3x+1\right)\left(x^2+3x-3\right)-5\)
\(=t\left(t-4\right)-5\)
\(=t^2-4t-5\)
tự làm nốt ý này nhé.
những ý kia lát nx mình làm.
d) \(x^4+5x^2+9\).Đặt \(x^2=t\) thì:
\(x^4+5x^2+9=t^2+5t+9\)
Làm nốt ý này nhé bạn! Ý kia chút nữa rảnh làm!
b) \(\left(3x-2\right)^2\left(6x-5\right)\left(6x-3\right)-5\)
\(=\left(3x-2\right)^2\left(6x-5\right)\left(6x-3\right)-\left(\sqrt{5}\right)^2\)
\(=\left(3x-2+\sqrt{5}\right)\left(3x-2-\sqrt{5}\right)\left(6x-5\right)\left(6x-3\right)\)
Câu b) mình làm nhầm,sorry bạn nhé!
c, \(x^4+6x^3+11x^2+6x+1\)
\(=\left(x^2\right)^2+2.x^2.3x+\left(3x\right)^2+2x^2+6x+1\)
\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)+1=\left(x^2+3x+1\right)^2\)
d, \(x^4+5x^2+9=\left(x^2\right)^2+2.x^2.3+3^2-x^2\)
\(=\left(x^2+3\right)^2-x^2=\left(x^2-x+3\right)\left(x^2+x+3\right)\)
a, Đặt \(x^2+3x-1=t\)
\(\left(x^2+3x+1\right)\left(x^2+3x-3\right)-5\)
\(=\left(t+2\right)\left(t-2\right)-5=t^2-9\)
\(=\left(t-3\right)\left(t+3\right)=\left(x^2+3x-4\right)\left(x^2+3x+2\right)\)
\(=\left[x\left(x+4\right)-\left(x+4\right)\right]\left[x\left(x+1\right)+2\left(x+1\right)\right]\)
\(=\left(x+4\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)\)
Câu b) bạn xem lại đề nhé~
\(x^4+6x^3+11x^2+6x+1\)
\(=\left(x^2\right)^2+\left(3x\right)^2+1^2+2.x^2.3x+2.3x.1+2.x^2.1\)
\(=\left(x^2+3x+1\right)^2\)
\(x^4+5x^2+9\)
\(=x^4+6x^2+9-x^2\)
\(=\left(x^2+3\right)^2-x^2\)
\(=\left(x^2+3-x\right)\left(x^2+x+3\right)\)
\(a^3\left(c-b^2\right)+b^3\left(a-c^2\right)+c^3\left(b-a^2\right)+abc\left(abc-1\right)\)
\(=a^3\left(c-b^2\right)+ab^3-b^3c^2+c^3b-c^3a^2+\left(abc\right)^2-abc\)
\(=a^3\left(c-b^2\right)+\left(bc^3-b^3c^2\right)-\left(c^3a^2-a^2b^2c^2\right)-\left(abc-ab^3\right)\)
\(=a^3\left(c-b^2\right)+bc^2\left(c-b^2\right)-a^2c^2\left(c-b^2\right)-ab\left(c-b^2\right)\)
\(=\left(c-b^2\right)\left(a^3+bc^2-a^2c^2-ab\right)\)
\(=\left(c-b^2\right)\left[a^2\left(a-c^2\right)-b\left(a-c^2\right)\right]\)
\(=\left(c-b^2\right)\left(a^2-b\right)\left(a-c^2\right)\)