Question

$\huge\color{purple}{\colorbox{orange}{Question}}$:- find the sum 2x² + 3x - 4 and 3x³ + 2​

Answer 1

Given expressions are,

$\longrightarrow 2x^2 + 3x - 4 \; \& \; 3x^2 + 2$

We have to add these two expressions.

Solution:

An expression is a mathematical symbol, or combination of symbols, representing a valid or relation. Example: 2 + 2 = 4.

Let us start solving the problem and understand the steps to get the final result.

$(2x^2 + 3x - 4) + (3x^2 + 2)$

Get rid the unnecessary parentheses,

$\implies 2x^2 + 3x - 4 + 3x^2 + 2$

Organize the similar terms,

$\implies (2 + 3)x^2 + 3x + (-4 + 2)$

Arrange the constant terms,

$\implies 5x^2 + 3x + (-2)$

We know that, (+) (-) = (-), so,

$\implies 5x^2 + 3x - 2$

Therefore the addition of 2x² + 3x - 4 and 3x³ + 2 is:

$\boxed{(2x^2 + 3x - 4) + (3x^2 + 2) = 5x^2 + 3x - 2}$

Answer 2

Answer:

Question :

• »» Find the sum 2x² + 3x - 4 and 3x³ + 2.

$\begin{gathered}\end{gathered}$

Solution :

$\rm{\implies{\bigg(2{x}^{2} + 3x - 4\bigg) + \bigg(3{x}^{2} + 2\bigg)}}$

$\rm{\implies{\bigg(2{x}^{2} +3{x}^{2} \bigg) +3x+ \bigg( - 4 + 2\bigg)}}$

$\rm{\implies{\bigg(2 + 3 \bigg){x}^{2}+3x + \bigg( - 4 + 2 \bigg)}}$

$\rm{\implies{(5){x}^{2}+3x + (-2)}}$

$\rm{\implies{5{x}^{2}+3x -2}}$

$\therefore \:{\underline{\boxed{\sf{\red{5{x}^{2}+3x -2}}}}} \qquad \sf\big(Ans \big)$

Hence, the sum of 2x² + 3x - 4 and 3x³ + 2 is 5x² + 3x - 2.

$\begin{gathered}\end{gathered}$

Learn More :

☼ Algebraic identities:-

• ➛ (a+b)²+(a-b)² = 2a²+2b²
• ➛ (a+b)²-(a-b)² = 4ab
• ➛ (a+b)(a -b) = a²-b²
• ➛ (a+b+c)² = a²+b²+c²+2ab+2bc+2ca
• ➛ (a-b)³ = a³-b³-3ab(a-b)
• ➛ (a³+b³) = (a+b)(a²-ab+b²)
• ➛ a²+b² = (a+b)²-2ab
• ➛ a³-b³ = (a-b)(a²+ab +b²)
• ➛ If a + b + c = 0 then a³ + b³ + c³ = 3abc

☼ BODMAS :

↝ BODMAS rule is an acronym used to remember the order of operations to be followed while solving expressions in mathematics.

It stands for :-

• »» B - Brackets,
• »» O - Order of powers or roots,
• »» D - Division,
• »» M - Multiplication 
• »» A - Addition
• »» S - Subtraction.

↝ It means that expressions having multiple operators need to be simplified from left to right in this order only.

☼ BODMAS RULE :

↝ First, we solve brackets, then powers or roots, then division or multiplication (whatever comes first from the left side of the expression), and then at last subtraction or addition.

• ↠ Addition (+)
• ↠ Subtraction (-)
• ↠ Multiplication (×)
• ↠ Division (÷)
• ↠ Brackets ( )

☼ EXPONENT :

↝ The exponent of a number says how many times to use the number in a multiplication.

☼ LAW OF EXPONENT :

The important laws of exponents are given below:

• ➠ ${\rm{{a}^{m} \times {a}^{n} = {a}^{m + n}}}$
• ➠ ${\rm{{a}^{m}/{a}^{n} = {a}^{m - n}}}$
• ➠ ${\rm{({a}^{m})^{n} = {a}^{mn}}}$
• ➠ ${\rm{{a}^{n}/{b}^{n} = ({a/b})^{n} }}$
• ➠ ${\rm{{a}^{0} = 1}}$
• ➠ ${\rm{{a}^{ - m} = {1/a}^{m}}}$
• ➠ ${\rm{{a}^{\frac{1}{n} } = \sqrt[n]{a}}}$

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