Math, asked by saumyasonal972, 7 months ago

0
CHAL
Factorise : 32x2 + 72y2 - 20022 - 96xy

Answers

Answered by elsalovesus

Answer:

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factorize49x^4-168x^2y^2+144y^4

49x4-168x2y2+144y4

Final result :

(7x2 - 12y2)2

Step 1 :

Equation at the end of step 1 :

((49•(x4))-((168•(x2))•(y2)))+(24•32y4)

Step 2 :

Equation at the end of step 2 :

((49 • (x4)) - ((23•3•7x2) • y2)) + (24•32y4)

Step 3 :

Equation at the end of step 3 :

(72x4 - (23•3•7x2y2)) + (24•32y4)

Step 4 :

Trying to factor a multi variable polynomial :

4.1 Factoring 49x4 - 168x2y2 + 144y4

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (7x2 - 12y2)•(7x2 - 12y2)

Detecting a perfect square :

4.2 49x4 -168x2y2 +144y4 is a perfect square

It factors into (7x2-12y2)•(7x2-12y2)

which is another way of writing (7x2-12y2)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Trying to factor as a Difference of Squares :

4.3 Factoring: 7x2-12y2

Put the exponent aside, try to factor 7x2-12y2

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 : 7 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Final result :

(7x2 - 12y2)2

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Terms and Topics

Identifying Perfect Squares

Factoring Multi Variable Polynomials

0CHALFactorise : 32x2 + 72y2 - 20022 - 96xy​

Answers

0
CHAL
Factorise : 32x2 + 72y2 - 20022 - 96xy