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a) (2a - b)(b + 4a) + 2a(b - 3a)
= 2a(b + 4a) - b(b + 4a) + 2ab - 6a^2
= 2ab + 8a^2 - b^2 - 4ab + 2ab - 6a^2
= (8a^2 - 6a^2) + (2ab + 2ab - 4ab) - b^2
= 2a^2 - b^2
b) .(3a - 2b)(2a - 3b) - 6a(a - b)
= 3a(2a - 3b) - 2b(2a - 3b) - (6a^2 - 6ab)
= 6a^2 - 9ab - (4ab - 6b^2) - (6a^2 - 6ab)
= 6a^2 - 9ab - 4ab + 6b^2 - 6a^2 + 6ab
= 6b^2 + (6a^2 - 6a^2) + (6ab - 4ab - 9ab)
= 6b^2 - 7ab
c. 5b(2x - b) - (8b - x)(2x - b)
= 10bx - 5b^2 - 8b(2x - b) + x(2x - b)
= 10bx - 5b^2 - 16bx + 8b^2 + 2x^2 - bx
= (10bx - 16bx - bx) + 2x^2 + (8b^2 - 5b^2)
= -7bx + 2x^2 + 3b^2
d. 2x(a + 15x) + (x - 6a)(5a + 2x)
= 2ax + 30x^2 + x(5a + 2x) - 6a(5a + 2x)
= 2ax + 30x^2 + 5ax + 2x^2 - 30a^2 - 12ax
= (30x^2 + 2x^2) + (2ax + 5ax - 12ax) - 30a^2
= 32x^2 - 5ax - 30a^2
Chúc bạn hok tốt !!!
a) \(\left(2a-b\right)\left(b+4a\right)+2a\left(b-3a\right)\)
\(=2ab+8a^2-b^2-4ab+2ab-6a^2\)
\(=\left(2ab+2ab-4ab\right)+\left(8a^2-6a^2\right)-b^2\)
\(=2a^2-b^2\)
b) \(\left(3a-2b\right).\left(2a-3b\right)-6a\left(a-b\right)\)
\(=6a^2-9ab-4ab+6b^2-6a^2+6ab\)
\(=\left(6a^2-6a^2\right)-\left(9ab+4ab-6ab\right)+6b^2\)
\(=-7ab+b^2\)
c) \(5b\left(2x-b\right)-\left(8b-x\right)\left(2x-b\right)\)
\(=10bx-5b^2-\left(16bx-8b^2-2x^2+bx\right)\)
\(=10bx-5b^2-16bx+8b^2+2x^2-bx\)
\(=\left(10bx-16bx-bx\right)-\left(5b^2-8b^2\right)+2x^2\)
\(=-7bx+3b^2+2x^2\)
d) \(2x\left(a+15x\right)+\left(x-6a\right)\left(5a+2x\right)\)
\(=2ax+30x^2+5ax+2x^2-30a^2-12ax\)
\(=\left(2ax+5ax-12ax\right)+\left(30x^2+2x^2\right)-30a^2\)
\(=-5ax+32x^2-30a^2\)
a: =2ab+8a^2-b^2-4ab+2ab-6a^2
=2a^2-b^2
b: =6a^2-9ab-4ab+6b^2-6a^2+6ab
=-7ab+6b^2
c: =10bx-5b^2-16bx+8b^2+2x^2-xb
=3b^2+2x^2-7xb
d: =2xa+30x^2+5ax+2x^2-30a^2-12ax
=32x^2-30a^2-5ax
\(\left(7x-4\right)\left(2x+3\right)-13x\)
\(=14x^2+21x-8x-12-13x\)
\(=14x^2-12\)
\(a^3-\left(a^2-3a\right)\left(a+3\right)\)
\(=a^3-\left(a^3+3a^2-3a^2-9a\right)\)
\(=a^3-a^3-3a^2+3a^2+9a\)
\(=9a\)
\(\left(2a-b\right)\left(b+4a\right)+2a\left(b-3a\right)\)
\(=2ab+8a^2-b^2-4ab+2ab-6a^2\)
\(=\)\(2a^2-b^2\)
\(5b\left(2x-b\right)+\left(x-6a\right)\left(5a+2x\right)\)
\(=10bx-5b^2+5ax+2x^2-30a^2-12ax\)
\(=2x^2-30a^2-5b^2+10bx-7ax\)
mik cần gấp
Bài 1:
\(a,\dfrac{1}{2}x^2y^2\left(2x+y\right)\left(x^2-xy+1\right)=\left(x^3y^2+\dfrac{1}{2}x^2y^3\right)\left(x^2-xy+1\right)=x^5y^2-x^4y^3+x^3y^2+\dfrac{1}{2}x^3y^3-\dfrac{1}{2}x^3y^4+\dfrac{1}{2}x^2y^3\)
\(b,\left(\dfrac{1}{2}x-1\right)\left(2x-3\right)=x^2-\dfrac{3}{2}x-2x+3=x^2-\dfrac{7}{2}x+3\)\(c,\left(x-7\right)\left(x-5\right)=x^2-5x-7x+35=x^2-12x+35\)\(f,\left(x-\dfrac{1}{2}\right)\left(x+\dfrac{1}{2}\right)\left(4x-1\right)=\left(x^2-\dfrac{1}{4}\right)\left(4x-1\right)=4x^3-x^2-x+\dfrac{1}{4}\)Bài 2 ,
\(\left(x-1\right)\left(x^2+x+1\right)=x^3+x^2+x-x^2-x-1=x^3-1\Rightarrowđpcm\)\(b,\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)=x^4+x^3y+x^2y^2+y^3x+x^3y-x^2y^2-xy^3-y^4=x^4-y^4\)
e) = \(\dfrac{3}{2\left(x+3\right)}\) - \(\dfrac{x-6}{2x\left(x+3\right)}\)
= \(\dfrac{3x}{2x\left(x+3\right)}\) - \(\dfrac{x-6}{2x\left(x+3\right)}\) = \(\dfrac{3x-x+6}{2x\left(x+3\right)}\)
= \(\dfrac{2x-6}{2x\left(x+3\right)}\)
= \(\dfrac{2\left(x-3\right)}{2x\left(x+3\right)}\)
c) = \(\dfrac{2\left(a^3-b^3\right)}{3\left(a+b\right)}\) . \(\dfrac{6\left(a+b\right)}{a^2-2ab+b^2}\)
= \(\dfrac{-2\left(a+b\right)\left(a^2-2ab+b^2\right)}{3\left(a+b\right)}\) . \(\dfrac{6\left(a+b\right)}{a^2-2ab+b^2}\)
= \(\dfrac{-2\left(a+b\right)}{1}\) . \(\dfrac{2}{1}\) = -4 (a+b)
\(\left(2x+1\right)^2-2\left(2x+1\right)\left(3-x\right)+\left(x-3\right)^2\)
\(=\left(2x+1\right)^2+2\left(2x-1\right)\left(x-3\right)+\left(x-3\right)^2\)
\(=\left(2x+1+x-3\right)^2\)
\(=\left(3x-2\right)^2\)
------------------------------------
\(a^3+3a^2-6a-8\)
\(=a^3+4a^2-a^2-4a-2a-8\)
\(=\left(a^3+4a^2\right)-\left(a^2+4a\right)-\left(2a+8\right)\)
\(=a^2\left(a+4\right)-a\left(a+4\right)-2\left(a+4\right)\)
\(=\left(a+4\right)\left(a^2-a-2\right)\)
\(=\left(a+4\right)\left(a^2-2a+a-2\right)\)
\(=\left(a+4\right)\left[\left(a^2-2a\right)+\left(a-2\right)\right]\)
\(=\left(a+4\right)\left[a\left(a-2\right)+\left(a-2\right)\right]\)
\(=\left(a+4\right)\left(a-2\right)\left(a+1\right)\)
---------------------------------
\(2x^2-5x+2\)
\(=2x^2-4x-x+2\)
\(=\left(2x^2-4x\right)-\left(x-2\right)\)
\(=2x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(2x-1\right)\)
-----------------------------------------
\(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-\left(2x-4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x+2y-2\right)\)
-------------------------------------
\(a^2-1+4b-4b^2\)
\(=a^2-\left(1-4b+4b^2\right)\)
\(=a^2-\left(1-2b\right)^2\)
\(=\left(a-1+2b\right)\left(a+1-2b\right)\)
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\(a^4+6a^2b+9b^2-1\)
\(=\left(a^4+6a^2b+9b^2\right)-1\)
\(=\left(a^2+3b\right)^2-1\)
\(=\left(a^2+3b-1\right)\left(a^2+3b+1\right)\)
---------------------------------
\(2x^3+16y^3\)
\(=2\left(x^3+8y^3\right)\)
\(=2\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
Lần sau ghi đề tách riêng từng câu ra nhé em. Ghi dính chùm vậy khó nhìn lắm. Sẽ ít ai giải cho em