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1.Use suitable identities to find the following products :
i)\((x + 4)(x + 10)\)
ii)\((x + 8)(x - 10)\)
iii)\((3x - 4)(3x - 5)\)
iv)\((y^2 + 3/2)(y^2 - 3/2)\)
v)\((3 - 2x)(3 + 2x)\)
Answer :

i)\((x + 4)(x + 10)\)
Using identity (iv), i.e.,\((x + a)(x + b) = x^2 + (a + b)x + ab\)
We have, \((x + 4)(x + 10) = x^2 + (4 + 10)x + (4)(10)\)
\(= x^2 + 14x + 40\)

ii)\((x + 8)(x - 10)\)
Using identity (iv), i.e.,\((x + a)(x + b) = x^2 + (a + b)x + ab\)
We have, \((x + 8)(x - 10) = x^2 + (8 - 10)x + (8)(-10)\)
\(= x^2 - 2x - 80\)

iii)\((3x + 4)(3x - 5)\)
Using identity (iv), i.e.,\((x + a)(x + b) = x^2 + (a + b)x + ab\)
We have, \((3x + 4)(3x - 5) = (3x)^2 + (4 - 5)x + (4)(5)\)
\(= 9x^2 - x + 20\)

iv)\((y^2 + 3/2)(y^2 - 3/2)\)
Using identity (iii), i.e.,\((a^2 - b^2) = (a + b)(a - b)\)
We have, \((y^2 + 3/2)(y^2 - 3/2) = (y^2)^2 - (3/2)^2\)
\(= y^4 - 9/4\)

v)\((3 - 2x)(3 + 2x)\)
Using identity (iii), i.e.,\((a^2 - b^2) = (a + b)(a - b)\)
We have, \((3 - 2x)(3 + 2x) = (3)^2 - (2x)^2)\)
\(= 9 - 4x^2\)