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Question:

Find the following squares by using the identities: (i)(b−7)² (ii)(xy+3z)² (iii)(6x²−5y)² (iv)(23m+32n)² (v)(0.4p−0.5q)² (vi)(2xy+5y)²

Solution:

i)(b−7)²=b²+7²−2(b)(7)=b²+49−14b [(a−b)²=a²+b²−2ab]
ii)(xy+3z)²=(xy)²+(3z)²+2(xy)(3z)=x²y²+9z²+6xyz [(a+b)²=a²+b²+2ab]
iii)(6x²−5y)²=(6x²)²+(5y)²−2(6x²)(5y)=36x⁴+25y²−60x²y [(a−b)²=a²+b²−2ab]
iv)(23m+32n)²=(23m)²+(32n)²+2(23m)(32n)=529m²+1024n²+1472mn [(a+b)²=a²+b²+2ab]
v)(0.4p−0.5q)²=(0.4p)²+(0.5q)²−2(0.4p)(0.5q)=0.16p²+0.25q²−0.4pq [(a−b)²=a²+b²−2ab]
vi)(2xy+5y)²=(2xy)²+(5y)²+2(2xy)(5y)=4x²y²+25y²+20xy² [(a+b)²=a²+b²+2ab]=y²(4x²+20x+25)