\(\left(x+1\right)\left(x^2-x-x^2+x-1\right)=-\left(x+1\right)\)

\(\left(2a^2+1\right)^2-4a^2-\left(2a^2+1\right)^2=-4a^2\)

\(\left(a^2+b^2+c^2+a^2-b^2-c^2\right)\left(a^2+b^2+c^2-a^2+b^2+c^2\right)=2a^2\left(2b^2+2c^2\right)=4a^2b^2+4a^2c^2\)

\(\left(a-5\right)^2\left(a+5\right)^2=\left(a^2-25\right)^2\)

\(\left(3a^3+1\right)^2-9a^2-\left(3a^3+1\right)^2=-9a^2\)

a) Áp dụng hằng đẳng thức : \(a^2-b^2+\left(a-b\right)\left(a+b\right)\)

Ta có ; \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)\)

\(=\left[\left(a^2+2a\right)+3\right]\left[\left(a^2+2a\right)-3\right]\)

\(=\left(a^2+2a\right)^2-3^2\)

\(=\left(a^2+2a\right)^2-9\)

c: \(5\left(a+b\right)+x\left(a+b\right)\)

=(a+b)(x+5)

d: \(\left(a-b\right)^2-\left(b-a\right)\)

\(=\left(a-b\right)^2+\left(a-b\right)\)

=(a-b)(a-b+1)

e: \(=\left(12x^2+6x\right)\left(y+z+y-z\right)\)

\(=2y\cdot6x\cdot\left(2x+1\right)=12xy\left(2x+1\right)\)

1) a) A= (x+2)(\(x^2-2x+4\)) -(\(x^3-2\))

=(x+2)(\(x^2-2x+2^2\))-(\(x^3-2\))

= \(x^3+2^3\)-\(x^3+2\)

=(\(x^3-x^3\))+(\(2^3+2\))

=10

b) B= (a+2)(a-2)(\(a^2+2a+4\))(\(a^2-2a+4\))

= \(a^2-2^2\)+\(a^2+\left(2a\right)^2+4^2\)

=\(a^2-4+a^2+4a^2+16\)

=(\(a^2+a^2+4a^2\))+(-4+16)

=\(6a^2\)+12

bn chép lại đề nhé

a/ \(=\left(x+y\right)^2-4x^2y^2=\left(x+y+2xy\right)\left(x+y-2xy\right)\)

b/ \(=\left(2bc+b^2+c^2-a^2\right)\left(2bc-b^2-c^2+a^2\right)\)

\(=\left[\left(b+c\right)^2-a^2\right]\left[-\left(b+c\right)^2+a^2\right]\)

\(=\left(b+c-a\right)\left(b+c+a\right)^2\left(a-b-c\right)\)

c/ \(=2a^2+2b^2-2c^2+4ab=2\left[\left(a^2+b^2+2ab\right)-c^2\right]\)

\(=2\left(a+b-c\right)\left(a+b+c\right)\)

d/ \(=\left(4x^2-25\right)^2-9\left(4x^2-20x+25\right)\)

\(=\left(4x^2-25\right)^2-9\left(4x^2+25\right)+180x\)

tới đây bạn đặt a= 4x^2 -25 rồi làm típ nha, mình lười quá >< 

e/ tương tự câu d nha bạn

f/ \(=a^4\left(a^2-1\right)+2a^2\left(a+1\right)\)

\(=a^4\left(a-1\right)\left(a+1\right)+2a^2\left(a+1\right)\)

\(=a^2\left(a+1\right)\left(a^2+2\right)\)

g/   đặt \(a=3x^2+3x+2\) khi đó biểu thức trở thành

\(a^2-\left(a+4\right)^2=a^2-a^2-8a-16\)

\(=-8a-16=-8\left(3x^2+3x+2-8\right)=-8\left(3x^2+3x-6\right)\)

\(=-24\left(x^2+x-2\right)=-24\left(x-1\right)\left(x+2\right)\)

xong rùi nha bn. Chúc bn hc tốt (xin lỗi tại có mấy câu mình lười nha)

\(x^2-4x^2y^2+y^2+2xy\)

\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)

\(=\left(x+y\right)^2-4x^2y^2\)

\(=\left(x-2xy+y\right)\left(x+2xy+y\right)\)