Factorize the following expressions.(i) y2 + 2y – 48(ii) d2 – 4d

1.	Factorize the following expressions.(i) y2 + 2y – 48(ii) d2 – 4d – 45(iii) m2 + 16m + 63(iv) n2 – 19n – 92(v) p2 – 10p + 16(vi) x2 + 4x – 45
Answer» (i) y² + 2y – 48 y² + 2y – 48 = y² + 8y - 6y – 48 = y(y + 8) – 6(y + 8) = (y + 8) (y – 6) (ii) d² – 4d – 45 d² – 4d – 45 = d² – 9d + 5 d – 45 = d (d – 9) + 5 (d – 9) = (d – 9) (d + 5) (iii) m² + 16m + 63 m² + 16m + 63 = m² + 9m + 7m + 63 = m (m + 9) + 7 (m + 9) = (m + 9) (m + 7) (iv) n² – 19n – 9² n² – 19n – 92 = n² – 23n + 4n – 92 = n (n – 23) + 4 (n – 23) = (n – 23) (n + 4) (v) p² – 10p + 16 p² – 10p + 16 = p² – 8p – 2p + 16 = p (p – 8) – 2(p – 8) = (p – 8) (p – 2) (vi) x² + 4x – 45 x² + 4x – 45 = x² + 9x – 5x – 45 = x (x + 9) – 5(x + 9) = (x + 9) (x – 5)

Factorize the following expressions.(i) y2 + 2y – 48(ii) d2 – 4d – 45(iii) m2 + 16m + 63(iv) n2 – 19n – 92(v) p2 – 10p + 16(vi) x2 + 4x – 45

Answer»

(i) y² + 2y – 48

y² + 2y – 48
= y² + 8y - 6y – 48
= y(y + 8) – 6(y + 8)
= (y + 8) (y – 6)

(ii) d² – 4d – 45

d² – 4d – 45
= d² – 9d + 5 d – 45
= d (d – 9) + 5 (d – 9)
= (d – 9) (d + 5)

(iii) m² + 16m + 63

m² + 16m + 63
= m² + 9m + 7m + 63
= m (m + 9) + 7 (m + 9)
= (m + 9) (m + 7)

(iv) n² – 19n – 9²

n² – 19n – 92
= n² – 23n + 4n – 92
= n (n – 23) + 4 (n – 23)
= (n – 23) (n + 4)

(v) p² – 10p + 16

p² – 10p + 16
= p² – 8p – 2p + 16
= p (p – 8) – 2(p – 8)
= (p – 8) (p – 2)

(vi) x² + 4x – 45

x² + 4x – 45
= x² + 9x – 5x – 45
= x (x + 9) – 5(x + 9)
= (x + 9) (x – 5)