Solve (4x+y)^14,t

$$( 4 x + y ) ^ { 14 } , t$$

Least Common Multiple

$$t\left(268435456x^{14}[phone]x^{6}y^{8}+2050048x^{5}y^{9}+256256x^{4}y^{10}+23296x^{3}y^{11}+1456x^{2}y^{12}+56xy^{13}+y^{14}[phone]y^{6}x^{8}[phone]y^{5}x^{9}[phone]y^{4}x^{10}[phone]y^{3}x^{11}[phone]y^{2}x^{12}[phone]yx^{13}[phone]\left(xy\right)^{7}\right)$$

Solution Steps

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$t\left(268435456x^{14}[phone]x^{7}y^{7}[phone]x^{6}y^{8}+2050048x^{5}y^{9}+256256x^{4}y^{10}+23296x^{3}y^{11}+1456x^{2}y^{12}+56xy^{13}+y^{14}[phone]y^{6}x^{8}[phone]y^{5}x^{9}[phone]y^{4}x^{10}[phone]y^{3}x^{11}[phone]y^{2}x^{12}[phone]yx^{13}\right)$$

Expand the expression.

$$268435456tx^{14}[phone]tx^{7}y^{7}[phone]tx^{6}y^{8}+2050048tx^{5}y^{9}+256256tx^{4}y^{10}+23296tx^{3}y^{11}+1456tx^{2}y^{12}+56txy^{13}+ty^{14}[phone]ty^{6}x^{8}[phone]ty^{5}x^{9}[phone]ty^{4}x^{10}[phone]ty^{3}x^{11}[phone]ty^{2}x^{12}[phone]tyx^{13}$$

Evaluate

$$\left(4x+y\right)^{14},t$$