Question

Factorise the expressions

(i) ax² + bx

(ii) 7p² + 21q²

(iii) 2x³ + 2xy² + 2xz²

(iv) am² + bm² + bn² + an²

(v) (lm + l) + m + 1

(vi) y(y + z) + 9(y + z)

(vii) 5y² − 20y − 8z + 2yz

(viii) 10ab + 4a + 5b + 2

(ix) 6xy − 4y + 6 − 9x

Answer 1

(i) ax² + bx = a × x × x + b × x = x(ax + b)

(ii) 7p² + 21q² = 7 × p × p + 3 × 7 × q × q = 7(p² + 3q²)

(iii) 2x³ + 2xy² + 2xz² = 2x(x² + y² + z²)

(iv) am² + bm² + bn² + an² = am² + bm² + an² + bn²

= m²(a + b) + n²(a + b)

= (a + b) (m² + n²)

(v) (lm + l) + m + 1 = lm + m + l + 1

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

= (l + l) (m + 1)

(vi) y (y + z) + 9 (y + z) = (y + z) (y + 9)

(vii) 5y² − 20y − 8z + 2yz = 5y² − 20y + 2yz − 8z

= 5y(y − 4) + 2z(y − 4)

= (y − 4) (5y + 2z)

(viii) 10ab + 4a + 5b + 2 = 10ab + 5b + 4a + 2

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

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

(ix) 6xy − 4y + 6 − 9x = 6xy − 9x − 4y + 6

= 3x(2y − 3) − 2(2y − 3)

= (2y − 3) (3x − 2)
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