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# 2. Factorise. (i) $$4p^2 – 9q^2$$ (ii) $$63a^2 – 112b^2$$ (iii) $$49x^2 – 36$$ (iv) $$16x^5 – 144x^3$$ (v) $$(l + m)^2 – (l – m)^2$$ (vi) $$9x^2y^2 – 16$$ (vii) $$(x^2 – 2xy + y^2) – z^2$$ (viii) $$25a^2 – 4b^2 + 28bc – 49c^2$$

(i)Given: $$4p^2 – 9q^2$$

$$= (2p)^2 – (3q)^2$$

$$= (2p – 3q) (2p + 3q)\quad$$[∵ $$a^2 – b^2 = (a + b)(a – b)$$]

(ii)Given: $$63a^2 – 112b^2$$

$$= 7(9a^2 – 16b^2)$$

$$= 7 [(3a)^2 – (4b)^2]$$

$$= 7(3a – 4b)(3a + 4b)\quad$$[∵ $$a^2 – b^2 = (a + b)(a – b)$$]

(iii) Given:$$49x^2 – 36$$

$$49x^2 – 36 = (7x)^2 – (6)^2$$

$$= (7x – 6) (7x + 6)\quad$$[∵ $$a^2 – b^2 = (a + b)(a – b)$$]

(iv)Given: $$16x^5 – 144x^3 = 16x^3 (x^2 – 9)$$

$$= 16x^3 [(x)^2 – (3)^2]$$

$$= 16x^3(x – 3)(x + 3)\quad$$[∵ $$a^2 – b^2 = (a + b)(a – b)$$]

(v) Given:$$(l + m)^2 – (l – m)^2$$

$$= (l + m) – (l – m)] [(l + m) + (l – m)]\quad$$[∵ $$a^2 – b^2 = (a + b)(a – b)$$]

$$= (l + m – l + m)(l + m + l – m)$$

$$= (2m) (2l)$$

$$= 4ml$$

(vi)Given $$9x^2y^2 – 16 = (3xy)^2 – (4)^2$$

$$= (3xy – 4)(3xy + 4)\quad$$[∵ $$a^2 – b^2 = (a + b)(a – b)]$$

(vii)Given: $$(x^2 – 2xy + y^2) – z^2$$

$$= (x – y)^2 – z^2$$

$$= (x – y – z) (x – y + z)\quad$$[∵ $$a^2 – b^2 = (a + b)(a – b)]$$

(viii) Given:$$25a^2 – 4b^2 + 28bc – 49c^2$$

$$= 25a^2 – (4b^2 – 28bc + 49c^2)$$

$$= (5a)^2 – (2b – 7c)^2$$

$$= [5a – (2b – 7c)] [5a + (2b – 7c)]$$

$$= (5a – 2b + 7c)(5a + 2b – 7c)$$