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3.Find the following squares by using the identities.
(i) \((b – 7)^2\)

(ii) \((xy + 3z)^2\)

(iii) \((6x^2 – 5y)^2\)

(iv) \((\frac { 2 }{ 3 } m + \frac { 3 }{ 2 } n)^2\)

(v) \((0.4p – 0.5q)^2\)

(vi) \((2xy + 5y)^2\)


Answer :

(i)Given: \((b – 7)^2\)

\(=(b)^2-2(b)(7)+(7)^2\quad\)[using \((a-b)^2=a^2-2ab+b^2\)]

\(=(b)^2-14b+49\)

(ii)Given: \((xy+3z)^2\)

\(=(xy)^2+2(xy)(3z)+(3z)^2\quad\)[using \((a+b)^2=a^2+2ab+b^2\)]

\(=x^2y^2+6xyz+9y^2\)

(iii)Given:\((6x^2 – 5y)^2\)

\(=(6x^2)^2-2(6x^2)(5y)+(5y)^2\quad\)[using \((a-b)^2=a^2-2ab+b^2\)]

\(=36x^4-60x^2y+25y^2\)

(iv)Given: \((\frac { 2 }{ 3 } m + \frac { 3 }{ 2 } n)^2\)

\(=(\frac { 2 }{ 3 } m)^2+2(\frac { 2 }{ 3 } m)(\frac { 3 }{ 2 } n)+(\frac { 3 }{ 2 } n)^2\quad\)[using \((a+b)^2=a^2+2ab+b^2\)]

\(=\frac { 4 }{ 9 } m^2+2mn+\frac { 9 }{ 4 } n^2\)

(v)Given: \((0.4p – 0.5q)^2\)

\(=(0.4p)^2-2(0.4p)(0.5q)+(0.5q)^2\quad\)[using \((a-b)^2=a^2-2ab+b^2\)]

\(=0.16p^2-0.4pq+0.25q^2\)

(vi)Given: \((2xy+5y)^2\)

\(=(2xy)^2+2(2xy)(5y)+(5y)^2\quad\)[using \((a+b)^2=a^2+2ab+b^2\)]

\(=4x^2y^2+20xy^2+25y^2\)