question_answer

Factorise

(a) \[{{x}^{2}}+\text{ }xy+8x+8y~\]

(b) \[15xy-6x+5y-2\]

(c) \[ax+bx-ayby\]

Answer:

(a) \[{{x}^{2}}+xy+8x|+8y=x\times x+x\times y+\text{ }8\times x+8\times y\]

\[=x(x+y)+8\text{ }(x+y)\]

\[=(x+y)\text{ }(x+\text{ }8)\]

(b)

\[15xy\text{ }6x+\text{ }5y2=3\times 5\times x\times y2\times 3\]

\[\times x+5\times 1\times y2\times 1\]

\[=3\times x(5\times y2)+1\text{ }(5\times y2)\]

\[=3x(5y2)+1\text{ }(5y2)\]

\[=(5y2)\text{ }(3x+1)\]

(c)

\[ax+bxayby=a\times x+b\times xa\times yb\times y\]

\[=x(a+b)\text{ }y(a+b)\]

\[=\text{ }(a+b)\text{ }(xy)\]