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NCERT Solutions Class 8 Mathematics Solutions for Exercise 9.5 in Chapter 9 - Algebraic Expressions and Identities
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Q3) Find the following squares by using identities:
(i) \left(b-7\right)^2
(ii) \left(xy+3z\right)^2
(iii) \left(6x^2-5y\right)^2
(iv) \left(\frac{2}{3}m+\frac{3}{2}n\right)^2
(v) \left(0.4p-0.5q\right)^2
(vi) \left(2xy+5y\right)^2
Solution:
(i) \left(b-7\right)^2=\left(b\right)^2-2\times b\times7+\left(7\right)^2
[Using identity \left(a-b\right)^2=a^2-2ab+b^2]
= b^2-14b+49
(ii) \left(xy+3z\right)^2=\left(xy\right)^2+2\times xy\times3z+\left(3z\right)^2
[Using identity \left(a+b\right)^2=a^2+2ab+b^2
= x^2y^2+6xyz+9z^2
(iii) \left(6x^2-5y\right)^2
= \left(6x^2\right)^2-2\times6x^2\times5y+\left(5y\right)^2
[Using identity \left(a-b\right)^2=a^2-2ab+b^2]
= 36x^4-60x^2y+25y^2
(iv) \left(\frac{2}{3}m+\frac{3}{2}n\right)^2
= \left(\frac{2}{3}m\right)^2+2\times\frac{2}{3}m\times\frac{3}{2}n+\left(\frac{3}{2}n\right)^2
[Using identity \left(a+b\right)^2=a^2+2ab+b^2]
= \frac{4}{9}m^2+2mn+\frac{9}{4}n^2
(v) \left(0.4p-0.5q\right)^2
= \left(0.4p\right)^2-2\times0.4p\times0.5q+\left(0.5q\right)^2
[Using identity \left(a-b\right)^2=a^2-2ab+b^2]
= 0.16p^2-0.40pq+0.25q^2
(vi) \left(2xy+5y\right)^2
= \left(2xy\right)^2+2\times2xy\times5y+\left(5y\right)^2
[Using identity \left(a+b\right)^2=a^2+2ab+b^2]
= 4x^2y^2+20xy^2+25y^2
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