Giải:
a) \(\left(x-5\right)^2-16\)
\(=\left(x-5-4\right)\left(x-5+4\right)\)
\(=\left(x-9\right)\left(x-1\right)\)
b) \(25-\left(3-x\right)^2\)
\(=\left(5-3+x\right)\left(5+3-x\right)\)
\(=\left(2+x\right)\left(8-x\right)\)
c) \(49\left(y-4\right)^2-9\left(y+2\right)^2\)
\(=\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2\)
\(=\left[7\left(y-4\right)-3\left(y+2\right)\right]\left[7\left(y-4\right)+3\left(y+2\right)\right]\)
\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)\)
\(=\left(4y-34\right)\left(10y-22\right)\)
d) \(11x+11y-x^2-xy\)
\(=11\left(x+y\right)-x\left(x+y\right)\)
\(=\left(11-x\right)\left(x+y\right)\)
e) \(x^2-xy-8x+8y\)
\(=x\left(x-y\right)-8\left(x-y\right)\)
\(=\left(x-8\right)\left(x-y\right)\)
Vậy ...
\(\left(x-5\right)^2-16\)
\(=\left(x-5\right)^2-4^2\)
\(=\left(x-5-4\right)\left(x-5+4\right)\)
\(=\left(x-9\right)\left(x-1\right)\)
\(25-\left(3-x\right)^2\)
\(=5^2-\left(3-x\right)^2\)
\(=\left(5+3-x\right)\left(5-3+x\right)\)
\(=\left(8-x\right)\left(2+x\right)\)
\(49\left(y-4\right)^2-9\left(y+2\right)^2\)
\(=7^2\left(y-4\right)^2-3^2\left(y+2\right)^2\)
\(=\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2\)
\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)
\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)\)
\(=\left(4y-34\right)\left(10y-22\right)\)
\(11x+11y-x^2-xy\)
\(=11\left(x+y\right)-x\left(x+y\right)\)
\(=\left(11-x\right)\left(x+y\right)\)
\(x^2-xy-8x+8y\)
\(=x\left(x-y\right)-8\left(x-y\right)\)
\(=\left(x-8\right)\left(x-y\right)\)
a. \(\left(x-5\right)^2-16=\left(x-5-4\right)\left(x-5+4\right)=\left(x-9\right)\left(x-1\right)\)
b.\(25-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3-x\right)=\left(2+x\right)\left(8-x\right)\)
d.\(11x+11y-x^2-xy=11\left(x+y\right)-x\left(x+y\right)=\left(x+y\right)\left(11-x\right)\)
e.\(x^2-xy-8x+8y=x\left(x-y\right)-8\left(x-y\right)=\left(x-y\right)\left(x-8\right)\)
