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Question

Use a suitable identity to get each of the following products.

(i) (x+3)(x+3)

(ii) (2y+5)(2y+5)
(iii) (2a7)(2a7)
(iv) (3a12)(3a12)
(v) (1.1m0.4)(1.1m+0.4)
(vi) (a2+b2)(a2+b2)
(vii) (6x7)(6x+7)
(viii) (a+c)(a+c)
(ix) (x2+3y4)(x2+3y4)
(x) (7a9b)(7a9b)

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Solution

(i) Given (x+3)(x+3)=(x+3)2 [a×a=a2]
=x2+32+2(x)(3) [(a+b)2=a2+b2+2ab]
(x+3)(x+3)=x2+9+6x


(ii) Given (2y+5)(2y+5)=(2y+5)2 [a×a=a2]
=(2y)2+(5)2+2(2y)(5) [(a+b)2=a2+b2+2ab]
(2y+5)(2y+5)=4y2+25+20y

(iii) Given (2a7)(2a7)=(2a7)2
=(2a)2+(7)22(2a)(7) [(ab)2=a2+b22ab]
(2a7)(2a7)=4a2+4928a
(iv) Given (3a12)(3a12)=(3a12)2
=(3a)2+(12)2(2)3a(12) [(ab)2=a2+b22ab]
(3a12)(3a12)=9a2+143a
(v) Given (1.1m0.4)(1.1m+0.4)=(1.1m)2(0.4)2
[(a+b)(ab)=(a2b2)]
(1.1m0.4)(1.1m+0.4)=1.21m20.16


(vi) Given (a2+b2)(a2+b2)=(b2+a2)(b2a2)
=(b2)2(a2)2 [(a+b)(ab)=(a2b2)]
(a2+b2)(a2+b2)=b4a4

(vii) Given (6x7)(6x+7)=(6x)2(7)2 [(a+b)(ab)=(a2b2)]
(6x7)(6x+7)=36x249

(viii) (a+c)(a+c) =(a+c)2
=(a)2+c22(a)(c) [(ab)2=a2+b22ab]
(a+c)(a+c)=a22ac+c2
(ix) Given (x2+3y4)(x2+3y4)
=(x2+3y4)2
=(x2)2+2(x2)(3y4)+(3y4)2
=x24+3xy4+9y216 [(a+b)2=a2+b2+2ab]

(x) Given (7a9b)(7a9b)=(7a9b)2
=(7a)2+(9b)22(7a)(9b) [(ab)2=a2+b22ab]
=49a2+81b2126ab

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