$(a+b)^2 = a^2+b^2+2ab$

When two literals $a$ and $b$ represent two terms in algebraic form. The sum of them is written as $a+b$ in mathematics. It is an algebraic expression and also a binomial. The square of sum of them or binomial is written in mathematics as follows.

$(a+b)^2$

The square of sum of two terms is equal to the $a$ squared plus $b$ squared plus $2$ times product of $a$ and $b$.

$(a+b)^2$ $\,=\,$ $a^2+b^2+2ab$

In mathematics, the $a$ plus $b$ whole squared algebraic identity is called in three ways.

- The square of sum of two terms identity.
- The square of a binomial rule.
- The special binomial product formula.

In mathematics, the square of the sum of two terms is used as a formula in two cases.

The square of the sum of two terms is expanded as the sum of squares of both terms and two times the product of them.

$\implies$ $(a+b)^2 \,=\, a^2+b^2+2ab$

The sum of squares of the two terms and two times the product of them is simplified as the square of the sum of two terms.

$\implies$ $a^2+b^2+2ab \,=\, (a+b)^2$

$(1) \,\,\,$ Find $(3x+4y)^2$

Now, take $a = 3x$ and $b = 4y$ and substitute them in the expansion of the formula for evaluating its value.

$\implies$ $(3x+4y)^2$ $\,=\,$ $(3x)^2+(4y)^2+2(3x)(4y)$

$\implies$ $(3x+4y)^2$ $\,=\,$ $9x^2+16y^2+2 \times 3x \times 4y$

$\implies$ $(3x+4y)^2$ $\,=\,$ $9x^2+16y^2+24xy$

$(2) \,\,\,$ Simplify $p^2+25q^2+10pq$

$\implies$ $p^2+25q^2+10pq$ $\,=\,$ $p^2+(5q)^2+10pq$

$\implies$ $p^2+25q^2+10pq$ $\,=\,$ $p^2+(5q)^2+2 \times 5 \times p \times q$

$\implies$ $p^2+25q^2+10pq$ $\,=\,$ $p^2+(5q)^2+2 \times p \times 5 \times q$

$\implies$ $p^2+25q^2+10pq$ $\,=\,$ $p^2+(5q)^2+2 \times p \times 5q$

$\implies$ $p^2+25q^2+10pq$ $\,=\,$ $p^2+(5q)^2+2(p)(5q)$

Now, take $a = p$ and $b = 5q$, and simplify the algebraic expression by the $(a+b)^2$ identity

$\implies$ $p^2+25q^2+10pq$ $\,=\,$ $(p+5q)^2$

The $a$ plus $b$ whole square identity can be derived in mathematics in two different methods.

Learn the algebraic approach to derive the expansion of the $a+b$ whole square formula by the multiplication.

Learn the geometric method to derive the expansion of the $a+b$ whole squared identity by the areas of geometric shapes.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.