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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) \(6xy – 4y + 6 – 9x\)


Answer :

(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:\(6xy – 4y + 6 – 9x\)

\(= 6xy – 4y – 9x + 6\)

\(= 2y(3x – 2) – 3(3x – 2)\)

\(= (3x – 2) (2y – 3)\)