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Find the product using appropriate ident...

Find the product using appropriate identities
(i) (x+5)(x+5) (ii) (x+4)(x-4) (iii) (x+5)(x+3) (iv) (x-5)(x+3)

Text Solution

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(i) We know that `(x+y)^(2)=x^(2)+2xy+y^(2)`
Now, `(x+5)(x+5)=(x+5)^(2)=x^(2)+2xx x xx5+5^(2)=x^(2)+10x+25`
(ii) We know that `(x+a)(x-a)=x^(2)-a^(2)`
Now, `(x+4)(x-4)=x^(2)-4^(2)=x^(2)-16`
(iii) We know that `(x+a)(x+b)=x^(2)+(a+b)x+ab`
Now, `(x+5)(x+3)=x^(2)+(5+3)x+5xx3=x^(2)+8x+15`
(iv) We know that `(x-a)(x+b)=x^(2)+(-a+b)x+(-a)xxb`
Now, `(x-5)(x+3)=x^(2)+(-5+3)x+(-5)xx3=x^(2)-2x-15`
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