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Answer :
(i)We have: \((x + 3) (x + 7)\)
\(=x^2 + (3 + 7)x + 3\times 7\)
\(= x^2 +10x + 21\)
(ii)We have: \((4x + 5) (4x + 1)\)
\(=(4x)^2 + (5 + 1)(4x) + 5\times 1\)
\(= 16x^2 +24x + 5\)
(iii)We have: \((4x - 5) (4x - 1)\)
\(=(4x)^2 - (5 + 1)(4x) + (-5)\times(-1)\)
\(= 16x^2 -24x + 5\)
(iv)We have: \((4x + 5) (4x - 1)\)
\(=(4x)^2 + (5 - 1)(4x) + (5)\times(-1)\)
\(= 16x^2 +16x - 5\)
(v)We have: \((2x + 5y) (2x + 3y)\)
\(=(2x)^2 + (5y +3y)(2x) + (5y)\times (3y)\)
\(=(2x)^2 + (8y)(2x) + (5y)\times (3y)\)
\(= 4x^2 +16xy + 15y^2\)
(vi)We have: \((2a^2 + 9) (2a^2 + 5)\)
\(=(2a^2)^2 + (9+5)(2a^2) + (5)\times (9)\)
\(=(2a^2)^2 + (14)(2a^2) + 45\)
\(= 4a^4 +28a^2 + 45\)
(vii)We have: \((xyz - 4) (xyz - 2)\)
\(=(xyz)^2 - (4+2)(xyz) + (-4)\times (-2)\)
\(=(xyz)^2 - (6)(xyz) + 8\)
\(= x^2y^2z^2 -6xyz + 8\)