\(a,\left(-4xy-5\right)\left(5-4xy\right)=\left(4xy+5\right)\left(4xy-5\right).\)

\(=\left(4xy\right)^2-5^2=16x^2y^2-25\)

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

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

\(c,\left(3x-4\right)^2+2\left(3x-4\right)\left(4-x\right)+\left(4-x\right)^2\)

\(=\left[\left(3x-4\right)+\left(4-x\right)\right]^2\)

\(=\left(3x-4+4-x\right)^2=\left(2x\right)^2=4x^2\)

\(d,\left(a^2+ab+b^2\right)\left(a^2-ab+b^2\right)-\left(a^4+b^4\right)\)

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

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

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

\(\left(x+y\right)^3=x^3+3x^2y+3xy^2-y^3\)

\(\left(x-y\right)^3=x^3-3x^2y+3xy^2-y^3\)

\(\left(2y-3\right)^3=8y^3-36y^2+54y-27\)

a: Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)

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

\(=6x^2y+2y^3\)

a) $(3x+5)^2\\=(3x)^2+2.3x.5+5^2\\=9x^2+30x+25$

b) $(6x+\dfrac{1}{3})^2\\=(6x)^2+2.6x.\dfrac{1}{3}+(\dfrac{1}{3})^2\\=36x^2+4x+\dfrac{1}{9}$

c) $(5x-4y)^2\\=(5x)^2-2.5x.4y+(4y)^2\\=25x^2-40xy+16y^2$

d) $(5x-3)(5x+3)\\=(5x)^2-(3)^2\\=25x^2-9$

a: Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)

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

\(=6x^2y+2y^3\)

\(\left(x+y\right)^3-\left(x-y\right)^3\)

\(=\left(x+y-x+y\right)^3+3\left(x+y\right)\left(x-y\right)\left(x+y-x+y\right)\)

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

\(=8y^3+6x^2y-6y^3\)

\(=2y^3+6x^2y\)

\(a,\left(6x+5y\right)\left(6x-5y\right)\)

\(=\left(6x\right)^2-\left(5y\right)^2\)

\(=36x^2-25x^2\)

\(b,\left(-4xy-5\right)\left(5-4xy\right)\)

\(=-\left(5+4xy\right)\left(5-4xy\right)\)

\(=-[5^2-\left(4xy\right)^2]\)

\(=-\left(25-16xy^2\right)\)

\(c,\left(3x-4\right)^2+2.\left(3x-4\right).\left(4-x\right)+\left(4-x\right)^2\)

\(=\left(3x-4\right)\left(3x-4+2\right)\left(4-x\right)\left(1+4-x\right)\)

\(=\left(3x-4\right)\left(3x-2\right)\left(4-x\right)\left(5-x\right)\)

C

c

a: \(=-\left[\left(\dfrac{1}{3}ab^2+2a^3b\right)^3\right]\)

\(=\dfrac{-1}{27}a^3b^6-3\cdot\dfrac{1}{9}a^2b^4\cdot2a^3b-3\cdot\dfrac{1}{3}ab^2\cdot4a^6b^2-8a^9b^3\)

\(=\dfrac{-1}{27}a^3b^6-\dfrac{2}{3}a^5b^5-4a^7b^4-8a^9b^3\)

b: \(=x^3+3x^2+3x+1-x^3+3x^2-3x+1-6\left(x^2-1\right)\)

\(=6x^2+2-6x^2+6\)

=8