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# Factorize: $2{a^2} + bc - 2ab - ac$

Last updated date: 18th Jun 2024
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The standard form of a quadratic equation is $a{x^2} + bx + c$ , the given equation in the standard form will be $2{a^2} - 2ab - ac + bc$ or $2{a^2} + ( - 2b + c)a + bc$ . We can factorize this equation by taking the common terms out and then simplifying the expression.
$\Rightarrow 2{a^2} + bc - 2ab - ac = a(2a - c) - b(2a - c) \\ \Rightarrow 2{a^2} + bc - 2ab - ac = (a - b)(2a - c) \\$
Hence, the factored form of $2{a^2} + bc - 2ab - ac$ is $(a - b)(2a - c)$ .
Note: Factors of an equation are simply the expressions that completely divide the given equation. The standard form of a quadratic equation is $a{x^2} + bx + c = 0$ . To find the factors of the given equation, we get the values of a, b and c by comparing the given equation with the standard form. Then we will try to write b as a sum of two numbers such that their product is equal to the product of a and c, that is, ${b_1} \times {b_2} = a \times c$ , this method is known as factorization. We find the value of ${b_1}$ and ${b_2}$ by hit and trial. By putting the obtained equation equal to zero, we can find the value of “a” in terms of “b” and “c”.