Five times the sum of three times $x$ and $y$ whole square plus six times sum of three times $x$ and $y$ minus eight is the given mathematical expression.
The given algebraic expression matches with the form of a quadratic expression but the factor $3x+4$ in first and second terms makes the algebraic expression complex.
It can be expressed to our known quadratic form for our convenience by representing the factor $3x+4$ by a variable. So, let’s denote the factor $3x+4$ by a variable $z$.
Consider the first term $5z^2$ and the constant term $8$. Now, multiply both of them to find their product.
$5z^2 \times 8 \,=\, 40z^2$
The middle term is $6z$ in the given algebraic expression and let’s verify whether the product $40z^2$ can be split as either sum or difference of two terms, which should be equal to the middle term.
The product $40z^2$ can be split as a product of $10z$ and $4z$.
$\implies$ $40z^2 \,=\, 10z \times 4z$
The sum of the factors $10z$ and $4z$ is not equal to the middle term of the quadratic expression but their difference is equal to the middle term.
So, let’s split the middle term $6z$ as a difference of $10z$ and $4z$ in the algebraic expression.
It is time to factorize the algebraic expression by grouping the terms.
Now, let’s take the common factor out from the terms to factorise the algebraic expression.
$=\,\,\,$ $5z \times z$ $+$ $2 \times 5z$ $-$ $4z$ $-$ $8$
$=\,\,\,$ $5z \times (z+2)$ $-$ $4 \times z$ $-$ $4 \times 2$
$=\,\,\,$ $5z \times (z+2)$ $-$ $4 \times (z+2)$
The given algebraic expression is successfully factored but it is factored in terms of $z$. Actually, the algebraic expression is given in terms of a variable $x$. Hence, it should be converted in terms of $x$ from $z$.
$=\,\,\,$ $(3x+y+2)\big(5 \times (3x+y)-4\big)$
Now, distribute the factor $5$ over the addition of the terms $3x$ and $4$ as per the distributive property of multiplication over addition.
$=\,\,\,$ $(3x+y+2)(5 \times 3x+5 \times y-4)$
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the maths problems in different methods with understandable steps.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved