1.

16*b^2 %2B 25*a^2 %2B 40*(a*b)

Answer»

25a^2 + 40ab + 16b^2

= (5a)^2 + 2*5*4*ab + (4b)^2

[using (a + b)^2 = a^2 + b^2 + 2ab]

= (5a + 4b)^2

= (5a + 4b)(5a + 4b)

Enter a problem...

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Factor 25a^2-40ab+16b^2

25a2−40ab+16b225a2-40ab+16b2

Rewrite25a225a2as(5a)2(5a)2.

(5a)2−40ab+16b2(5a)2-40ab+16b2

Rewrite16b216b2as(4b)2(4b)2.

(5a)2−40ab+(4b)2(5a)2-40ab+(4b)2

Check the middletermby multiplying2ab2aband compare this result with the middletermin the originalexpression.

2ab=2⋅(5a)⋅(−4b)2ab=2⋅(5a)⋅(-4b)

Simplify.

2ab=−40ab2ab=-40ab

Factorusing theperfect squaretrinomialrulea2−2ab+b2=(a−b)2a2-2ab+b2=(a-b)2, wherea=5aa=5aandb=−4bb=-4b.

(5a−4b)2

25a^2 +40ab+16b^2

=(5a)^2+2*5*4*ab+(4b)^2

[using(a+b)^2=a^2+b^2+2ab]

=(5a+4b)^2

=(5a+4b)(5a+4b)


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