Ncert solutions

Ncert solutions

Grade 8

Factorisation | Exercise 14.2

Question 1

Q1) Factorise the following expressions.

(i) a^2+8a+16

(ii) p^2-10p+25

(iii) 25m^2+30m+9

(iv) 49y^2+84yz+36z^2

(v) 4x^2-8x+4

(vi) 121b^2\ -\ 88bc\ +16c^2

(vii) \left(l+m\right)^2-4lm

(viii) 25a^2-4b^2+28bc-49c^2

Solution 1:

(i)\left(a\right)^2+\ 2\times2\times2\times a\ +\left(2\times2\right)^2

a^2\ +\ 2\times4\times a\ +4^2

= \left(a+4\right)^2

(ii) p^2-5p-5p+25

p(p-5) -5 (p-5)

(p-5) (p-5)

(iii) 25m^2+30m\ +9

5m\left(5m+3\right)+3\left(5m+3\right)

(5m+3) (5m+3)

(iv) \left(7y\right)^2+2\times7\times y\times6\times z\ +\ \left(6z\right)^2

\left(7y\right)^2+2\ \left(7y\right)\ \left(6z\right)\ +\left(6z\right)^2

\left(7y+6z\right)^2

(v) \left(2x\right)^2-2\times2\times x\times2\ +\ 2^2

\left(2x\right)^2-2\left(2x\right)\left(2\right)+2^2

\left(2x-2\right)^2

(vi) \left(11b\right)^2-2\times\left(11b\right)\times8c+\left(8c\right)^2

\left(11b-8c\right)^2

(vii) l^2+m^2+2lm-4lm

l^2+m^2-2lm

\left(l-m\right)^2

(viii) \left(5a\right)^2-\left(2b\right)^2+2\times2b\times7c-\left(7c\right)^2

\left(5a\right)^2-\left[\left(2b-7c\right)^2\right]

\left(5a\right)^2-\left(2b-7c\right)^2

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subject-cta

Question 1

Q1) Factorise the following expressions.

(i) a^2+8a+16

(ii) p^2-10p+25

(iii) 25m^2+30m+9

(iv) 49y^2+84yz+36z^2

(v) 4x^2-8x+4

(vi) 121b^2\ -\ 88bc\ +16c^2

(vii) \left(l+m\right)^2-4lm

(viii) 25a^2-4b^2+28bc-49c^2

Solution 1:

(i)\left(a\right)^2+\ 2\times2\times2\times a\ +\left(2\times2\right)^2

a^2\ +\ 2\times4\times a\ +4^2

= \left(a+4\right)^2

(ii) p^2-5p-5p+25

p(p-5) -5 (p-5)

(p-5) (p-5)

(iii) 25m^2+30m\ +9

5m\left(5m+3\right)+3\left(5m+3\right)

(5m+3) (5m+3)

(iv) \left(7y\right)^2+2\times7\times y\times6\times z\ +\ \left(6z\right)^2

\left(7y\right)^2+2\ \left(7y\right)\ \left(6z\right)\ +\left(6z\right)^2

\left(7y+6z\right)^2

(v) \left(2x\right)^2-2\times2\times x\times2\ +\ 2^2

\left(2x\right)^2-2\left(2x\right)\left(2\right)+2^2

\left(2x-2\right)^2

(vi) \left(11b\right)^2-2\times\left(11b\right)\times8c+\left(8c\right)^2

\left(11b-8c\right)^2

(vii) l^2+m^2+2lm-4lm

l^2+m^2-2lm

\left(l-m\right)^2

(viii) \left(5a\right)^2-\left(2b\right)^2+2\times2b\times7c-\left(7c\right)^2

\left(5a\right)^2-\left[\left(2b-7c\right)^2\right]

\left(5a\right)^2-\left(2b-7c\right)^2

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