# 4 Algebra Tips Guaranteed To Improve Your Test Grades

Algebra is
one such section where the students often do silly mistakes. Some textbooks of NCERTalso have complex algebra sums which become a bit difficult for the
students and during calculation they end up making mistakes. To avoid this and
to score well there are some shortcut tricks and tips that will enhance their
algebra solving skills. Math cannot be taken as a burden. Students should
concentrate and enjoy while solving sums.

There are
some steps which are to be followed in the conventional method and is lengthy.
Those steps can be skipped by using techniques. 4 major tips or techniques to
solve Algebra are:

●

For example:

[latex]-2x+5-16x^{2}-10x^{3}=-10[/latex]

[latex]-1(-2x+5-16x^{2}-10x^{3})=-1(-10)[/latex]

[latex]2x-5+16x^{2}+10x^{3}=10[/latex]

Many times there is an uneven distribution of -1 and this is the reason of major mistakes. The change of sign is also an effective idea in solving algebraic equations. The positive signs are to be changed to negative and vice-versa.

For example:

[latex]-2x+5-16x^{2}-10x^{3}=-10[/latex]

[latex]2x-5+16x^{2}+10x^{3}=10[/latex]

**Sign Change versus to multiply by -1:**The negative signs in an equation looks too complicated in an algebraic expression which adds confusion for the students to solve. In an expression where negative signs are more than positive term the first thing that the student can do is multiply both the sides by -1. This will cancel out a maximum of the negatives.For example:

[latex]-2x+5-16x^{2}-10x^{3}=-10[/latex]

[latex]-1(-2x+5-16x^{2}-10x^{3})=-1(-10)[/latex]

[latex]2x-5+16x^{2}+10x^{3}=10[/latex]

Many times there is an uneven distribution of -1 and this is the reason of major mistakes. The change of sign is also an effective idea in solving algebraic equations. The positive signs are to be changed to negative and vice-versa.

For example:

[latex]-2x+5-16x^{2}-10x^{3}=-10[/latex]

[latex]2x-5+16x^{2}+10x^{3}=10[/latex]

●

For example:

2x-10=6

2x=16

x=8

This is a simple equation but this method is applicable for complex algebraic equations too. The equations can simply be changed without showing the step which is not that necessary.

**To Move Left/Right versus Subtract and Add both sides:**When there are examples where addition and subtraction are done to both sides often there occurs some mistake. In order to avoid that changing the sides of the equations is the best way.For example:

2x-10=6

2x=16

x=8

This is a simple equation but this method is applicable for complex algebraic equations too. The equations can simply be changed without showing the step which is not that necessary.

●

For example:

cos(7x)

sin(7x)

The function here is same so throughout the problem, be it a complex one, the procedure will be same. To avoid complexity in complex problems major mistakes which take place is while copying the problem or copying sin and cos in every single step. It is convenient to use C & S in place of sin and cos

For example:

[latex]cos ^{2}+sin^{2}[/latex]

[latex]C ^{2}+S^{2}[/latex]

This way the entire thing is not copied in every step so the possibility of error decreases. At the end, the students have to remember to write it back to the same form.

**To use C & S versus Sin x &cos x:**when the equation of sin x and cos x are of the same function.For example:

cos(7x)

sin(7x)

The function here is same so throughout the problem, be it a complex one, the procedure will be same. To avoid complexity in complex problems major mistakes which take place is while copying the problem or copying sin and cos in every single step. It is convenient to use C & S in place of sin and cos

For example:

[latex]cos ^{2}+sin^{2}[/latex]

[latex]C ^{2}+S^{2}[/latex]

This way the entire thing is not copied in every step so the possibility of error decreases. At the end, the students have to remember to write it back to the same form.

●

For example:

[latex]\frac{13x}{5} = \frac{20}{3x}[/latex]

[latex]5\times \frac{13x}{5} = 5\times \frac{20}{3x}[/latex]

[latex]13x=\frac{100}{3x}[/latex]

[latex]3x\times 13x=3x\times \frac{100}{3x}[/latex]

[latex]39x^{2}=100[/latex]

Here there are too many steps where the student needs to multiply and divide both sides to cancel terms and then simplify. But by cross multiplication the process becomes quite simple.

For example:

[latex]\frac{13x}{5} = \frac{20}{3x}[/latex]

[latex]13x\times 3x=20\times 5[/latex]

[latex]39x^{2}=100[/latex]

**To Cross Left/Right or Multiply Both Sides:**This trick can be used in every complex problem. We normally proceed with an equation like-For example:

[latex]\frac{13x}{5} = \frac{20}{3x}[/latex]

[latex]5\times \frac{13x}{5} = 5\times \frac{20}{3x}[/latex]

[latex]13x=\frac{100}{3x}[/latex]

[latex]3x\times 13x=3x\times \frac{100}{3x}[/latex]

[latex]39x^{2}=100[/latex]

Here there are too many steps where the student needs to multiply and divide both sides to cancel terms and then simplify. But by cross multiplication the process becomes quite simple.

For example:

[latex]\frac{13x}{5} = \frac{20}{3x}[/latex]

[latex]13x\times 3x=20\times 5[/latex]

[latex]39x^{2}=100[/latex]

The simple
tips and tricks will help the students to solve algebraic equations in a much
simpler way and will help them to score good grades at any level be it board
exams or any competitive exams likeJEE. All the student need is to be consistent. These tricks can
help to simplify and reduce the errors.

*About the author:**With a degree in Engineering, Shreyaa Banerjee is a content writer by profession. She is a voracious reader apart from writing and blogging along with part-time teaching. She is presently exploring all about the digital education with Byju’s-the Learning App.*