Given:
2(a2+ab)+3-ab
⇒ 2a2+2ab+3-ab
⇒ 2a2+2ab-ab+3
⇒ 2a2+ab+3
⇒ 2(5)2+(5)(-3)+3
⇒ 2×25-15+3 [putting a=5, b=-3]
⇒ 50-15+3
⇒ 38
If \( x, y \) are two positive integers such that \( x + y = 20 \) and the maximum value of \( x^3 y \) is \( k \) at \( x = a, y = \beta \), then \( \frac{k}{\alpha^2 \beta^2} = ? \)
Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.
(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.
(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30