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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 $$(a+b)^2=a^2+2ab+b^2$$]

$$=4x^2y^2+20xy^2+25y^2$$