Use a suitable identity to get each of the following products.
(i)(x+3)(x+3)
(ii)(2y+5)(2y+5)
(iii)(2a−7)(2a−7)
(iv)(3a−1/2)(3a−1/2)
(v)(1.1m−0.4)(1.1m+0.4)
(vi)(a²+b²)(−a²+b²)
(vii)(6x−7)(6x+7)
(viii)(−a+c)(−a+c)
(ix)(x²+3y⁴)(x²+3y⁴)
(x)(7a−9b)(7a−9b)

(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 (2a−7)(2a−7)=(2a−7)²=(2a)²+(7)²−2;(2a)(7) ≅[(a−b)²=a²+b²−2;ab] ≅(2a−7)(2a−7)=4a²+49−2;8a
(iv) Given (3a−1/2)(3a−1/2)=(3a−1/2)²=(3a)²+(1/2)²−(2)3a(1/2) ≅[(a−b)²=a²+b²−2;ab] ≅(3a−1/2)(3a−1/2)=9a²+1/4−3a
(v) Given (1.1m−0.4)(1.1m+0.4)=(1.1m)²−(0.4)² ≅[(a+b)(a−b)=(a²−b²)] ≅(1.1m−0.4)(1.1m+0.4)=1.21m²−0.16
(vi) Given (a²+b²)(−a²+b²)=(b²+a²)(b²−a²)=(b²)²−(a²)² ≅[(a+b)(a−b)=(a²−b²)] ≅(a²+b²)(−a²+b²)=b⁴−a⁴
(vii) Given (6x−7)(6x+7)=(6x)²−(7)² ≅[(a+b)(a−b)=(a²−b²)] ≅(6x−7)(6x+7)=36x²−49
(viii)(−a+c)(−a+c)=(−a+c)²=(−a)²+c²−2;(−a)(c) ≅[(a−b)²=a²+b²−2;ab] ≅(−a+c)(−a+c)=a²−2;ac+c²
(ix) Given (x²+3y⁴)(x²+3y⁴)=(x²+3y⁴)²=(x²)²+2(x²)(3y⁴)+(3y⁴)²=x⁸+6x²y⁴+9y⁸ ≅[(a+b)²=a²+b²+2ab]
(x) Given (7a−9b)(7a−9b)=(7a−9b)²=(7a)²+(9b)²−2;(7a)(9b) ≅[(a−b)²=a²+b²−2;ab]=49a²+81b²−1;26ab