Math, asked by lauratjacob, 2 months ago

Factorise: 50y^2 – 98

Answers

Answered by studytosuccess19
0

STEP

1

:

Equation at the end of step 1

(2•52y2) - 98 = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

50y2 - 98 = 2 • (25y2 - 49)

Trying to factor as a Difference of Squares:

3.2 Factoring: 25y2 - 49

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 25 is the square of 5

Check : 49 is the square of 7

Check : y2 is the square of y1

Factorization is : (5y + 7) • (5y - 7)

Equation at the end of step

3

:

2 • (5y + 7) • (5y - 7) = 0

STEP

4

:

Theory - Roots of a product

4.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Equations which are never true:

4.2 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Answered by anjugoyal954
3

Answer:

2(25y²-49)

2(5y²-7²)

2(5y-7) (5y+7)

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