Use suitable identities to find the following products:
(i) (x + 4)(x + 10)
(ii) (x + 8)(x – 10)
(iii) (3x + 4)(3x – 5)
(iv) (y2 + 3/2)(y2 - 3/2)
(i) (x+4)(x +10)
Using the identity, (x + a)(x + b) = x 2+(a + b)x + ab
[Here, a = 4 and b = 10]
We get,
(x+4)(x+10) = x2+(4+10)x+(4×10)
= x2+14x+40
(ii) (x + 8)(x – 10)
Using the identity, (x + a)(x + b) = x 2+(a + b)x + ab
[Here, a = 8 and b = −10]
We get,
(x + 8)(x − 10) = x2+(8+(−10))x+(8×(−10))
= x2+(8−10)x–80
= x2−2x−80
(iii) (3x+4)(3x–5)
Using the identity, (x+a)(x+b) = x 2+(a+b)x+ab
[Here, x = 3x, a = 4 and b = −5]
We get,
(3x+4)(3x−5) = (3x)2+[4+(−5)]3x+4×(−5)
= 9x2+3x(4–5)–20
= 9x2–3x–20
(iv) (y2+3/2)(y2-3/2)
Using the identity, (x+y)(x–y) = x2–y 2
[Here, x = y2and y = 3/2]
We get,
(y2+3/2)(y2–3/2) = (y2)2–(3/2)2
= y4–9/4