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Answer (1)
Problem 1: [tex]$\Large\boxed{\sf{(x + 3y + 5z)^2}}$[/tex]Square the first term: [tex]$\sf{x^2}$[/tex]Square of the second term: [tex]$\sf{(3y)^2 = 9y^2}$[/tex]Square the third term: [tex]$\sf{(5z)^2 = 25z^2}$[/tex]Multiply the product of the first and second term by 2: [tex]$\sf{2(x)(3y) = 6xy}$[/tex]Multiply the product of the first and third term by 2: [tex]$\sf{2(x)(5z) = 10xz}$[/tex]Multiply the product of the second and third term by 2: [tex]$\sf{2(3y)(5z) = 30yz}$[/tex]Answer: [tex]$\boxed{\sf{x^2 + 9y^2 + 25z^2 + 6xy + 10xz + 30yz}}$[/tex][tex]\\[/tex]Problem 2: [tex]$\Large{\boxed{\sf{(4a - 7b - 2c)^2}}}$[/tex]Square the first term: [tex]$\sf{(4a)^2 = 16a^2}$[/tex]Square of the second term: [tex]$\sf{(-7b)^2 = 49b^2}$[/tex]Square the third term: [tex]$\sf{(-2c)^2 = 4c^2}$[/tex]Multiply the product of the first and second term by 2: [tex]$\sf{2(4a)(-7b) = -56ab}$[/tex]Multiply the product of the first and third term by 2: [tex]$\sf{2(4a)(-2c) = -16ac}$[/tex]Multiply the product of the second and third term by 2: [tex]$\sf{2(-7b)(-2c) = 28bc}$[/tex]Answer: [tex]$\boxed{\sf{16a^2 + 49b^2 + 4c^2 - 56ab - 16ac + 28bc}}$[/tex][tex]\\[/tex]Problem 3: [tex]$\Large{\boxed{\sf{(-2p + 4q + 5)^2}}}$[/tex]Square the first term: [tex]$\sf{(-2p)^2 = 4p^2}$[/tex]Square of the second term: [tex]$\sf{(4q)^2 = 16q^2}$[/tex]Square the third term: [tex]$\sf{(5)^2 = 25}$[/tex]Multiply the product of the first and second term by 2: [tex]$\sf{2(-2p)(4q) = -16pq}$[/tex]Multiply the product of the first and third term by 2: [tex]$\sf{2(-2p)(5) = -20p}$[/tex]Multiply the product of the second and third term by 2: [tex]$\sf{2(4q)(5) = 40q}$[/tex]Answer: [tex]$\boxed{\sf{4p^2 + 16q^2 + 25 - 16pq - 20p + 40q}}$[/tex]
