1.

Factorize the following perfect squares. (a) x^{2} – 12x + 36 (b) 64a^{2} - 48ab + 9b^{2} (c) 16x^{2} + 40xy + 25y^{2} (d) a^{2} - 22ab + 121b^{2}

Answer» <html><body><p>Step-by-step explanation:(<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>) STEP 1 : Equation at the <a href="https://interviewquestions.tuteehub.com/tag/end-971042" style="font-weight:bold;" target="_blank" title="Click to know more about END">END</a> of step 1  ((64 • (a2)) -  48ab) +  32b2 STEP  2 : Equation at the end of step 2 :  (26a2 -  48ab) +  32b2 STEP <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a> : Trying to factor a multi variable polynomial 3.1    Factoring    64a2 - 48ab + 9b2   Try to factor this multi-variable trinomial using trial and error   Found a factorization  :  (8a - 3b)•(8a - 3b) Detecting a perfect square : 3.2    64a2  -48ab  +9b2  is a perfect square   It factors into  (8a-3b)•(8a-3b) which is another way of writing  (8a-3b)2 How to recognize a perfect square trinomial:   • It has three terms   • Two of its terms are perfect <a href="https://interviewquestions.tuteehub.com/tag/squares-1223400" style="font-weight:bold;" target="_blank" title="Click to know more about SQUARES">SQUARES</a> themselves   • The remaining term is <a href="https://interviewquestions.tuteehub.com/tag/twice-714133" style="font-weight:bold;" target="_blank" title="Click to know more about TWICE">TWICE</a> the product of the square roots of the other two termsFinal result :  (8a - 3b)2 (D)   STEP 1 : Equation at the end of step 1  ((a2) +  22ab) +  112b2 STEP 2 : Trying to factor a multi variable polynomial 2.1    Factoring    a2 + 22ab + 121b2   Try to factor this multi-variable trinomial using trial and error   Found a factorization  :  (a + 11b)•(a + 11b) Detecting a perfect square : 2.2    a2  +22ab  +121b2  is a perfect square   It factors into  (a+11b)•(a+11b) which is another way of writing  (a+11b)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 Final result :  (a + 11b)2</p></body></html>


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