Question

Factorize the following expression :-
${20x}^{2} + 60xy + {45y}^{2}$

HINT : Use the given-below formula in it.
${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$
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Answer 1

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

(20 • (x2)) - (32•5y2)

Step 2 :

Equation at the end of step 2 :

(22•5x2) - (32•5y2)

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

20x2 - 45y2 = 5 • (4x2 - 9y2)

Trying to factor as a Difference of Squares :

4.2 Factoring: 4x2 - 9y2

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 : 4 is the square of 2

Check : 9 is the square of 3

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (2x + 3y) • (2x - 3y)

Final result :

5 • (2x + 3y) • (2x - 3y)

Answer 2

Answer:

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Step-by-step explanation:

Factorize the following expression :-

${20x}^{2} + 60xy + {45y}^{2}$

HINT : Use the given-below formula in it.

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