I have 5 math questions for algebraic expressions, the first one i 1/4 (8x + 16), the second is 1/3 (3p + 12), The third is 1/2 (14k - 10), the 4th is 1/8 (8a - 24), and the last one is 1/2 (4p + 1)

Answer:See explanationStep-by-step explanation:The first function is [tex]\frac{1}{4}(8x+16)[/tex]You probably want to expand  so we need to apply the distributive property:This implies that:[tex]\frac{1}{4}(8x+16)=\frac{1}{4}*8x+\frac{1}{4}*16[/tex][tex]\implies \frac{1}{4}(8x+16)=2x+4[/tex]The second function is [tex]\frac{1}{3}(3p+12)[/tex].We again apply the distributive property to get:[tex]\frac{1}{3}(3p+12)=\frac{1}{3}*3p+\frac{1}{3}*12[/tex][tex]\implies \frac{1}{3}(3p+12)=p+4[/tex]The third one is [tex]\frac{1}{2}(14k-10)[/tex]We expand using the distributive property to get:[tex]\frac{1}{2}(14k-10)=\frac{1}{2}*14k-\frac{1}{2}*10[/tex][tex]\implies \frac{1}{2}(14k-10)=7k-5[/tex]The fourth is [tex]\frac{1}{8}(8a-24)[/tex]We expand to get:[tex]\frac{1}{8}(8a-24) =\frac{1}{8}*8a-\frac{1}{8}*24[/tex][tex]\frac{1}{8}(8a-24) =a-3[/tex]The fifth one is [tex]\frac{1}{2}(4p+1)[/tex]Expand to get:[tex]\frac{1}{2}(4p+1)=\frac{1}{2}*4p+\frac{1}{2}*1[/tex][tex]\frac{1}{2}(4p+1)=2p+\frac{1}{2}[/tex]