Question

The height of a triangle is (x4 + y4) and its base is 14xy. Find the area of the triangle. (Hint: Area of the triangle = 1/2 x base x height)

If p + q = 13 and pq = 22, then find p2 + q2.

Use suitable identities to get each of the following.

(1.1m – 0.4)(1.1m + 0.4)

(p/8 + 3q/4)(p/8 + 3q/4)

503 x 504

(2xy – 5y)2

Use the identity (x + a)(x + b) = x2 + (a + b)x + ab to find the following products.

(p + 10)(p + 11)

(9x – 5)(9x – 1)

(5y + 2x)(3y + 2x)

(9 + 2a2)(5 + 2a2)

Factorise the following expressions.

5xy – 25x3y2

x (3x – y) – 5(3x – y) – z(3x – y)

(a + b)(x + y) + (2a + 3)(x + y) – (3a + 4b)(x + y)

16p3 – 4p

16p2 – 40pq + 25q2

X8 – y8 ( Hint: write x8 as (x4)2 and y8 as (y4)2 )

Expand the following, using suitable identity.

(x2y – xy2)2

(2x + 9)(2x – 7)

Use the suitable identity to expand and simplify: (a + 1/a)2

If (x + 1/x) = 25, then find (x2 + 1/x2)

answers

Answer 1

area of triangle equal to 1 by 2 into base into height.
1/2(X^4+Y^4)14XY
7XY(X^4 Y^4)
7X^5Y+7Y^5X




p+q=13
(p+q)^2=(13)^2
p^2+q^2+2pq=169
p^2+q^2+2(22)=169
p^2+q^2+44=169
p^2+q^2=169-44
p^2+q^2=125




(a + b)(a-b) equal to a square minus b square
(1.1+0.4)(1.1-0.4)
(1.1)^2-(0.4)^2
1.21-0.16
1.05