Factorise the expressions.(i) ax² + bx(ii) 7p² + 21q²(iii) 2x³ + 2

1.	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» (i) ax² + bx Answer: x(ax + b) (ii) 7p² + 21q² Answer: 7(p² + 3q²) (iii) 2x³ + 2xy² + 2xz² Answer: 2x³ + 2xy² + 2xz² = 2x(x²+y²+z²) (iv) am² + bm² + bn² + an² Answer: a(m² + n²) + b(m² + n²) = (a + b)(m² + n²) (v) (lm + l) + m + 1 Answer: l(m + 1) + 1(m + 1) = (l + 1)(m + 1) (vi) y (y + z) + 9 (y + z) Answer: (y + 9)(y + z) (vii) 5y² – 20y – 8z + 2yz Answer: 5y(y + 4) + 2z(y + 4) = (5 + 2z)(y + 4) (viii) 10ab + 4a + 5b + 2 Answer: 5b + 10ab + 2 + 4a = 5b(1 + 2a) + 2(1 + 2a) = (5b + 2)(1 + 2a) (ix) 6xy – 4y + 6 – 9x Answer: 6xy – 4y + – 9x + 6 = 2y (3x – 2) - 3 (3x - 2) = (2y – 3)(3x – 2)

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»

(i) ax² + bx

Answer: x(ax + b)

(ii) 7p² + 21q²

Answer: 7(p² + 3q²)

(iii) 2x³ + 2xy² + 2xz²

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

(iv) am² + bm² + bn² + an²

Answer: a(m² + n²) + b(m² + n²)
= (a + b)(m² + n²)

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

Answer: l(m + 1) + 1(m + 1)
= (l + 1)(m + 1)

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

Answer: (y + 9)(y + z)

(vii) 5y² – 20y – 8z + 2yz

Answer: 5y(y + 4) + 2z(y + 4)
= (5 + 2z)(y + 4)

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

Answer: 5b + 10ab + 2 + 4a
= 5b(1 + 2a) + 2(1 + 2a)
= (5b + 2)(1 + 2a)

(ix) 6xy – 4y + 6 – 9x

Answer: 6xy – 4y + – 9x + 6
= 2y (3x – 2) - 3 (3x - 2)
= (2y – 3)(3x – 2)