How do I expand (2x+2)^2
2 Answers
sciencesolve | Teacher | (Level 3) Educator Emeritus
You should use binomial expansion `(a+b)^2 = a^2 + 2ab + b^2` , hence you should substitute 2x for a and 2 for b such that:
`(2x+2)^2 = (2x)^2 + 2(2x)2 + 2^2`
`(2x+2)^2 = 4x^2 + 8x + 4`
Hence, using binomial expansion yields`(2x+2)^2 = 4x^2 + 8x + 4` .
You may also write the square of binomial `2x + 2` as the product:
`(2x + 2)(2x + 2)`
Factoring out 2 in each brackets yields:
`2(x+1)*2(x+1) = 4(x+1)(x+1)`
Opening the brackets yields:
`4(x+1)(x+1) = 4(x^2 + x + x + 1)`
`4(x+1)(x+1) = 4x^2 + 4x + 4x + 4`
Collecting like terms yields:
4(x+1)(x+1) = 4x^2 + 8x + 4
Hence, expanding the binomial 2x + 2 by any methods yields `(2x+2)^2 = 4x^2 + 8x + 4` .
angels9286 | College Teacher | (Level 1) Honors
(2x+2)^2= 4(x+1)^2 = 4(x^2 +2x+1) = 4x^2+8x+4