Need to calculate: The factorization of the polynomial ax2+ay+bx2+by.

Question

Tasneem Almond · Accepted Answer

Formula used:
The factors of a polynomial can be found by taking a common factor and this method is called factor by grouping,

a b + a c + b d + c d = a (b + c) + d (b + c)

= (a + d) (b + c)

Or,

a b - a c + b d - c d = a (b - c) + d (b - c)

= (a + d) (b - c)

Calculation:
Consider the polynomial,

a x^{2} + a y + b x^{2} + b y

.
This is a four terms polynomial, factorization of this polynomial can be found by factor by grouping as,

a x^{2} + a y + b x^{2} + b y = (a x^{2} + a y) + (b x^{2} + b y)

= a (x^{2} + y) + b (x^{2} + y)

As,

(x^{2} + y)

is the common factor of the polynomial factor it out as follows,

a x^{2} + a y + b x^{2} + b y = a (x^{2} + y) + b (x^{2} + y)

= (x^{2} + y) (a + b)

The factorization of the polynomial

a x^{2} + a y + b x^{2} +

by is

(x^{2} + y) (a + b)

.
Check the result as follows,

(x^{2} + y) (a + b) = x^{2} * a + x^{2} * b + y * a + y * b

= a x^{2} + b x^{2} + a y + b y

= a x^{2} + a y + b x^{2} + b y

Thus, the factorization of the polynomial

a x^{2} + a y + b x^{2} +

by is

(x^{2} + y) (a + b)

.

Need to calculate: The factorization of the polynomial ax^{2}+ay+bx^{2}+by.