Factoring
Factored form of x2-10x+25
What is (x-5)2?
y=2(x-2)(x+4) in standard form.
What is y=-2x2-4x+16?
What is (x + a)(x + b)?
x2 + x(a + b) + ab
Find HCF and LCM of 13 and 17
HCF = 1 and LCM = 221
Factored form of 5x2 - 500
What is 5(x-10)(x+10)
Solve the equation x2+4x-5=0.
x=-5 & x=1
Write the expanded form for the expression: (x + 2y + z)2
x2 + 4y2 + z2 + 4xy + 4yz + 2zx.
Two cubes of edge 6 cm are joined to form a cuboid. Find the total surface area of the cuboid.
360 cm2
Factored form of 9x2 - 30x + 25
What is (3x-5)2
Rahul and Rohan have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. Find out how many marbles they had to start with.
x = 36 and x = 9
If x + y + z = 0, and x2 + y2 + z2 = 16, then find the value of xy + yz + xz.
xy + yz + zx = -8.
If α and β are the zeroes of the polynomial ax2 + bx + c, find the value of α2 + β2.
α2 + β2 = (b2 - 2ac)/a2
Factored form of 3xm - 3xn - m + n.
What is (3x-1)(m-n)?
Solve the quadratic equation 2x2 + x – 528 = 0, using quadratic formula.
x=16 or x=-33/2
Compute the expression (399)2 using algebraic identities.
159201
In an acute angled triangle ABC, if sin (A + B – C) = 1/2 and cos (B + C – A) = 1/√2, find ∠A, ∠B and ∠C.
∠A = 67.5°, ∠B = 37.5° and ∠C = 75°
Factored form of x2 - 8xy + 16y2 - 36m2
What is [(x-4y)+6m][(x-4y)-6m]?
Find the values of k for which the quadratic equation (3k + 1)x2 + 2(k + 1)x + 1 = 0 has equal roots. Also find the roots.
k = 0 or k = 1 and x = -1/2
The values of p and q if the solution to this system of equations is (-2,1). px+(9-q)y=10 (3p+1)-(q-6)y=-21.
What are p=-9/5 and q=113/5?
Determine the product of (3a + 2b) and (9a2 – 6ab + 4b2)
27a3 + 8b3
A thief runs away from a police station with a uniform speed of 100 m/minute. After one minute a policeman runs behind the thief to catch him. He goes at speed of 100 m/minute in first minute and increases his speed 10 m each succeeding minute. After how many minutes, the policeman will catch the thief?
5 mins