Question

factorise 16(x+y+z)²-16(x+y)²​

Answer 1

Answer:

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Step-by-step explanation:

$16(x+y+z) {}^{2} -16(x+y){}^{2} \\ \\ 16(x {}^{2} + y {}^{2} + z {}^{2} + 2xy + 2yz + 2zx) - 16(x {}^{2} + y {}^{2} + 2xy) \\ \\ 16x {}^{2} + 16y {}^{2} +16 z {}^{2} + 32xy + 32yz +3 2zx - (16x {}^{2} + 16y {}^{2} + 32xy) \\ \\ 16x {}^{2} + 16y {}^{2} +16 z {}^{2} + 32xy + 32yz +3 2zx - 16x {}^{2} - 16y {}^{2} - 32xy) \\ \\ \cancel{16x {}^{2}} \: \: \cancel{+ 16y {}^{2}} +16 z {}^{2} \: \: \cancel{+ 32xy} + 32yz +3 2zx \: \: \cancel{- 16x {}^{2}} \: \:\cancel{ - 16y {}^{2} } \: \: \cancel{- 32xy} \\ \\ 16z {}^{2} + 32yz + 32zx \\ \\ 16z(z + 2y + 2x)\\ \\(16z)(z + 2y + 2x)$