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= (2a)(2a) + (2a)(-2b) + (2a)(7c) + (-2b)(2a) + (-2b)(-2b) + (-2b)(7c) + (7c)(2a) +(7c)(-2b) + (7c)(7c)
= 4a^2 - 4ab + 14ac - 4ab + 4b^2 - 14bc + 14ac - 14bc + 49c^2
= 4a^2 + 4b^2 + 49c^2 - 8ab + 28ac - 28bc
7. (-x + 3y + 4z )(-x + 3y + 4z)
= (-x)(-x) + (-x)(3y) + (-x)(4z) + (3y)(-x) + (3y)(3y) + (3y)(4z) + (4z)(-x)+ (4z)(3y) + (4z )(4z)
= x^2 - 3xy - 4xz - 3xy + 9y^2 + 12yz - 4xz + 12yz + 16z^2
= x^2 + 9y^2 + 16z^2 - 6xy - 8xz + 24yz
8. - ( a + 2b - 3c)(a + 2b - 3c)
= - { (a)(a) + (a)(2b) +(a)(-3c) + (2b)(a) + (2b)(2b) + (2b)(-3c) + (-3c)(a) + (-3c)(2b) + (-3c)(-3c)}
= - { a^2 + 2ab - 3ac + 2ab + 4b^2 - 6bc - 3ac - 6bc + 9c^2 }
= - { a^2 + 4b^2 + 9c^2 + 4ab - 6ac - 12bc }
= - a^2 - 4b^2 - 9c^2 - 4ab + 6ac + 12bc
9. - (x - y + z)( x - y + z)
= - { (x)(x) + (x)(-y) + (x)(z) + (-y)(x) + (-y)(-y) + (-y)(z) + (z)(x) + (z)(-y) + (z)(z)}
= - { x^2 - xy + xz - xy + y^2 - yz + xz - yz + z^2 }
= - { x^2 + y^2 + z^2 - 2xy + 2xz - 2yz }
= - x^2 - y^2 - z^2 + 2xy - 2xz + 2yz
10. (3a - 3b - 3c) (3a - 3b - 3c)
= (3a)(3a) + (3a)(-3b) + (3a)(-3c) +(-3b)(3a) + (-3b)(-3b) + (-3b)(-3c) + (-3c)(3a) + (-3c)(-3b) + ( -3c)(-3c)
= 9a^2 - 9ab - 9ac - 9ab + 9b^2 + 9bc - 9ac + 9bc + 9c^2
= 9a^2 + 9b^2 + 9c^2 - 18ab - 18ac + 18bc