Define a trinomial quadratic expression and identify the coefficients a, b, and c in the expression 3x2−2x−5.

Factor the expression x(a+b)+y(a+b).

Find the factors of the trinomial quadratic expression x2+7x+10.

Find the factors of a2−8a+12.

Factorize the expression x2−7x−8.

Factorize a2−4ab−5b2 by considering it as a quadratic expression in 'a'.

Find the factors of the trinomial quadratic expression 3x2+14x+15.

Find the factors of 6x2+x−15.

Write the expression for the difference of two squares, x2−y2, as a product of its factors.

Factorize the expression 25a2−16b2.

Find the factors of 8x2−2 by first taking out the common numerical factor.

Factorize the expression (x+2)2−y2.

Find the factors of (a−2)2−(a+5)2.

The area of a rectangle is given by the expression x2+x−56. If the sides are binomial expressions with integer terms, find the expressions for its length and breadth.

Factorize the expression x4−16 by treating it as a difference of two squares multiple times.