Don't know where 6a came from?

[illmattic]

Line 1 = 4((3+a)²)+2(3+a)-3
Line 2 = 4(9+6a+a²)+6+2a-3

I understand everything going from Line 1 to Line 2 except where the 6a came from. Please show me the light.

Matt

 

[Deleted member 4993]

Line 1 = 4((3+a)²)+2(3+a)-3
Line 2 = 4(9+6a+a²)+6+2a-3

I understand everything going from Line 1 to Line 2 except where the 6a came from. Please show me the light.

Matt

Do you know the following identity:

(x + y)² = x² + 2 * x * y + y² .................... thus​

(3 + a)² = 3² + 2 * 3 * a + a² = 9 + 6a +a²​

Please post back in case of further doubt.

 

[Dr.Peterson]

Line 1 = 4((3+a)²)+2(3+a)-3
Line 2 = 4(9+6a+a²)+6+2a-3

I understand everything going from Line 1 to Line 2 except where the 6a came from. Please show me the light.

Matt

If you haven't learned that [MATH](x+y) = x^2 + 2xy + y^2[/MATH], then you can write [MATH](3+a)^2[/MATH] as [MATH](3+a)(3+a)[/MATH] and distribute ("FOIL"). What do you get?

 

[Steven G]

[math] (a+b)^2\neq a^2+b^2 \ so \ (3+a)^2 \neq 9+a^2[/math]

 

[illmattic]

Thanks for the clarification everyone. I didn't know the rules about exponents with parenthesis and foiling but I do now.

 

[HallsofIvy]

Have you learned the arithmetic law that "a(b+ c)= ab+ ac"?

That is what is being used: $(3+ a)^2= (3+ a)(3+ a)= (3+ a)(3)+ (3+ a)(a)$. Now do it again- $(3+ a)(3)= 3(3)+ a(3)= 9+ 3a$ and $(3+ a)a= 3a+ a^2$. Putting those together, $(3+ a)^2= 9+ 3a+ 3a+ a^2= 9+ 6a+ a^3$.