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# 3. Factorise the expressions. (i) $$ax^2 + bx$$ (ii) $$7p^2 + 21q^2$$ (iii) $$2x^3 + 2xy^2 + 2xz^2$$ (iv)$$am^2 + bm^2 + bn^2 + an^2$$ (v) $$(lm + l) + m + 1$$ (vi) $$y(y + z) + 9(y + z)$$ (vii) $$5y^2 – 20y – 8z + 2yz$$ (viii) $$10ab + 4a + 5b + 2$$ (ix) $$6xy – 4y + 6 – 9x$$

(i)Given: $$ax^2 + bx$$

$$= x(ax + 5)$$

(ii) Given:$$7p^2 + 21q^2$$

$$= 7(p^2 + 3q^2)$$

(iii) Given:$$2x^3 + 2xy^2 + 2xz^2$$

$$= 2x(x^2 + y^2 + z^2)$$

(iv)Given: $$am^2 + bm^2 + bn^2 + an^2$$

$$= m^2 (a + b) + n^2(a + b)$$

$$= (a + b)(m^2 + n^2)$$

(v)Given: $$(lm + l) + m + 1$$

$$= l(m + 1) + (m + 1)$$

$$= (m + 1) (l + 1)$$

(vi) Given:$$y(y + z) + 9(y + z)$$

$$= (y + z)(y + 9)$$

(vii)Given: $$5y^2 – 20y – 8z + 2yz$$

$$= 5y^2 – 20y + 2yz – 8z$$

$$= 5y(y – 4) + 2z(y – 4)$$

$$= (y – 4) (5y + 2z)$$

(viii)Given: $$10ab + 4a + 5b + 2$$

$$= 2a(5b + 2) + 1(5b + 2)$$

$$= (5b + 2)(2a + 1)$$

(ix)Given:$$6xy – 4y + 6 – 9x$$

$$= 6xy – 4y – 9x + 6$$

$$= 2y(3x – 2) – 3(3x – 2)$$

$$= (3x – 2) (2y – 3)$$