complete factorisation se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
First take out (3), and \(x^2-9\) is a difference of squares. In exams factorise the inside expression too.
Step 2
Why this answer is correct
The correct answer is A. (3(x-3)(x+3)) / correct complete form. First take out (3), and \(x^2-9\) is a difference of squares. In exams factorise the inside expression too.
Step 3
Exam Tip
पहले (3) निकालें और \(x^2-9\) वर्गों का अंतर है। परीक्षा में अंदर की अभिव्यक्ति को भी गुणनखंडित करें।
First take common factor (5), then factor \(x^2-4\). Exam tip: apply identities after taking the common factor.
Step 2
Why this answer is correct
The correct answer is B. (5(x-2)(x+2)). First take common factor (5), then factor \(x^2-4\). Exam tip: apply identities after taking the common factor.
Step 3
Exam Tip
पहले (5) सामान्य गुणनखंड लें और फिर \(x^2-4\) को तोड़ें। परीक्षा में सामान्य गुणनखंड के बाद पहचान लगाएं।
First take (4) common and (3x-2-5xy+2y-2=(3x-2y)(x-y)). In exams, factor the trinomial after the common factor.
Step 2
Why this answer is correct
The correct answer is A. (4(3x-2y)(x-y)). First take (4) common and (3x-2-5xy+2y-2=(3x-2y)(x-y)). In exams, factor the trinomial after the common factor.
Step 3
Exam Tip
पहले (4) सामान्य निकालें और (3x-2-5xy+2y-2=(3x-2y)(x-y)) है। परीक्षा में सामान्य गुणनखंड के बाद त्रिपद भी तोड़ें।
First take (a) common and then factor \(4a^2-9b^2\) by difference of squares. In exams, factorise completely.
Step 2
Why this answer is correct
The correct answer is A. (a(2a-3b)(2a+3b)). First take (a) common and then factor \(4a^2-9b^2\) by difference of squares. In exams, factorise completely.
Step 3
Exam Tip
पहले (a) सामान्य निकालें और फिर \(4a^2-9b^2\) को वर्गों के अंतर से तोड़ें। परीक्षा में पूरा गुणनखंडन करें।
First (x) is common and (2x-2+7x+3=(2x+1)(x+3)). In exams, factor the trinomial after taking the common factor.
Step 2
Why this answer is correct
The correct answer is A. (x(2x+1)(x+3)). First (x) is common and (2x-2+7x+3=(2x+1)(x+3)). In exams, factor the trinomial after taking the common factor.
Step 3
Exam Tip
पहले (x) सामान्य है और (2x-2+7x+3=(2x+1)(x+3)) है। परीक्षा में सामान्य गुणनखंड के बाद त्रिपद भी तोड़ें।
First (x-4-81=\(x^2-9\)\(x^2+9\)), and \(x^2-9\) factors further. In exams, factor further wherever possible.
Step 2
Why this answer is correct
The correct answer is B. ((x-3)(x+3)\(x^2+9\)). First (x-4-81=\(x^2-9\)\(x^2+9\)), and \(x^2-9\) factors further. In exams, factor further wherever possible.
Step 3
Exam Tip
पहले (x-4-81=\(x^2-9\)\(x^2+9\)) और \(x^2-9\) फिर टूटता है। परीक्षा में जहाँ संभव हो वहाँ आगे भी गुणनखंड करें।
First take (3y) common and then factorise \(4x^2-9y^2\). In exams, keep checking after taking the common factor.
Step 2
Why this answer is correct
The correct answer is A. (3y(2x-3y)(2x+3y)). First take (3y) common and then factorise \(4x^2-9y^2\). In exams, keep checking after taking the common factor.
Step 3
Exam Tip
पहले (3y) सामान्य निकालें और फिर \(4x^2-9y^2\) को गुणनखंडित करें। परीक्षा में सामान्य गुणनखंड के बाद भी जाँच जारी रखें।
First take (2) common and then apply difference of squares to \(4p^2-q^2\). In exams, factorise the final answer completely.
Step 2
Why this answer is correct
The correct answer is A. (2(2p-q)(2p+q)). First take (2) common and then apply difference of squares to \(4p^2-q^2\). In exams, factorise the final answer completely.
Step 3
Exam Tip
पहले (2) सामान्य निकालें और फिर \(4p^2-q^2\) पर वर्गों का अंतर लगाएँ। परीक्षा में अंतिम उत्तर को पूरी तरह गुणनखंडित करें।
The grouping gives (x-2(x-4)-1(x-4)), and \(x^2-1\) factors. In exams look for both common bracket and difference of squares.
Step 2
Why this answer is correct
The correct answer is A. ((x-4)(x-1)(x+1)) / सही रूप. The grouping gives (x-2(x-4)-1(x-4)), and \(x^2-1\) factors. In exams look for both common bracket and difference of squares.
Step 3
Exam Tip
समूह (x-2(x-4)-1(x-4)) बनता है और \(x^2-1\) टूटता है। परीक्षा में समान कोष्ठक और वर्गों का अंतर दोनों देखें।
The grouping gives (x-2(x+1)-1(x+1)), then \(x^2-1\) also factors. In exams check again after partial factorisation.
Step 2
Why this answer is correct
The correct answer is A. ((x+1)2(x-1)) / सही रूप. The grouping gives (x-2(x+1)-1(x+1)), then \(x^2-1\) also factors. In exams check again after partial factorisation.
Step 3
Exam Tip
समूह (x-2(x+1)-1(x+1)) बनता है, फिर \(x^2-1\) भी टूटता है। परीक्षा में आंशिक गुणनखंड के बाद फिर जांचें।
First take out (2x), and \(x^2-9\) is a difference of squares. In exams check the inside identity after the common factor.
Step 2
Why this answer is correct
The correct answer is A. (2x(x-3)(x+3)) / सही रूप. First take out (2x), and \(x^2-9\) is a difference of squares. In exams check the inside identity after the common factor.
Step 3
Exam Tip
पहले (2x) निकालें और \(x^2-9\) वर्गों का अंतर है। परीक्षा में समान गुणनखंड के बाद अंदर की पहचान देखें।
(x-4-y-4=\(x^2-y^2\)\(x^2+y^2\)), and \(x^2-y^2\) factors again. In exams check difference of squares twice.
Step 2
Why this answer is correct
The correct answer is B. ((x-y)(x+y)\(x^2+y^2\)) / सही पूर्ण रूप. (x-4-y-4=\(x^2-y^2\)\(x^2+y^2\)), and \(x^2-y^2\) factors again. In exams check difference of squares twice.
Step 3
Exam Tip
(x-4-y-4=\(x^2-y^2\)\(x^2+y^2\)) और \(x^2-y^2\) फिर टूटता है। परीक्षा में दो बार वर्गों का अंतर देखें।
First it is (\(x^2-y^2\)2), and (x-2-y-2=(x-y)(x+y)). In exams continue until complete factorisation.
Step 2
Why this answer is correct
The correct answer is B. ((x-y)2(x+y)2) / पूर्ण रूप. First it is (\(x^2-y^2\)2), and (x-2-y-2=(x-y)(x+y)). In exams continue until complete factorisation.
Step 3
Exam Tip
पहले यह (\(x^2-y^2\)2) है और (x-2-y-2=(x-y)(x+y)) है। परीक्षा में पूर्ण गुणनखंड तक जाएं।
It is (\(4x^2\)2-\(9y^2\)2), and \(4x^2-9y^2\) factors again. In exams check difference of squares repeatedly.
Step 2
Why this answer is correct
The correct answer is B. ((2x-3y)(2x+3y)\(4x^2+9y^2\)) / सही पूर्ण रूप. It is (\(4x^2\)2-\(9y^2\)2), and \(4x^2-9y^2\) factors again. In exams check difference of squares repeatedly.
Step 3
Exam Tip
यह (\(4x^2\)2-\(9y^2\)2) है और \(4x^2-9y^2\) फिर टूटता है। परीक्षा में बार-बार वर्गों का अंतर जांचें।
(x-4-16=\(x^2-4\)\(x^2+4\)) and (x-2-4=(x-2)(x+2)). In exams do not stop at partial factorisation.
Step 2
Why this answer is correct
The correct answer is B. ((x-2)(x+2)\(x^2+4\)) / पूर्ण रूप. (x-4-16=\(x^2-4\)\(x^2+4\)) and (x-2-4=(x-2)(x+2)). In exams do not stop at partial factorisation.
Step 3
Exam Tip
(x-4-16=\(x^2-4\)\(x^2+4\)) और (x-2-4=(x-2)(x+2)) है। परीक्षा में आंशिक गुणनखंड पर न रुकें।
\(a^6-b^6\) can be fully factored using both cube and square identities. Exam tip: factor both \(a^3-b^3\) and \(a^3+b^3\) further.
Step 2
Why this answer is correct
The correct answer is B. ( (a-b)(a+b)\(a^2+ab+b^2\)\(a^2-ab+b^2\) ). \(a^6-b^6\) can be fully factored using both cube and square identities. Exam tip: factor both \(a^3-b^3\) and \(a^3+b^3\) further.
Step 3
Exam Tip
\(a^6-b^6\) को घन और वर्ग दोनों पहचान से पूर्ण रूप में तोड़ा जा सकता है। परीक्षा में \(a^3-b^3\) और \(a^3+b^3\) दोनों को आगे तोड़ें।
First we get (\(x^2-1\)\(x^2-9\)), and both are differences of squares. Exam tip: factor till the final complete form.
Step 2
Why this answer is correct
The correct answer is C. ( (x-1)(x+1)(x-3)(x+3) ). First we get (\(x^2-1\)\(x^2-9\)), and both are differences of squares. Exam tip: factor till the final complete form.
Step 3
Exam Tip
पहले (\(x^2-1\)\(x^2-9\)) मिलता है और दोनों अंतर वर्ग हैं। परीक्षा में पूर्ण गुणनखंड रूप के लिए अंतिम तक तोड़ें।
First write \(x^4-16\) as (\(x^2\)2-42) and then factor \(x^2-4\). Exam tip: do not stop before the complete factorisation.
Step 2
Why this answer is correct
The correct answer is A. ( (x-2)(x+2)\(x^2+4\) ). First write \(x^4-16\) as (\(x^2\)2-42) and then factor \(x^2-4\). Exam tip: do not stop before the complete factorisation.
Step 3
Exam Tip
पहले \(x^4-16\) को (\(x^2\)2-42) लिखें और फिर \(x^2-4\) को भी तोड़ें। परीक्षा में पूर्ण गुणनखंड रूप तक रुकें नहीं।
First (a-4-16b-4=\(a^2-4b^2\)\(a^2+4b^2\)), then \(a^2-4b^2\) factors further. Exam tip: stop only after complete factorisation.
Step 2
Why this answer is correct
The correct answer is B. ((a-2b)(a+2b)\(a^2+4b^2\)). First (a-4-16b-4=\(a^2-4b^2\)\(a^2+4b^2\)), then \(a^2-4b^2\) factors further. Exam tip: stop only after complete factorisation.
Step 3
Exam Tip
पहले (a-4-16b-4=\(a^2-4b^2\)\(a^2+4b^2\)), फिर \(a^2-4b^2\) टूटता है। परीक्षा में पूर्ण गुणनखंड तक रुकें।
First take (5) common and split \(x^2-9\) by difference of squares. Exam tip: look further after common factor.
Step 2
Why this answer is correct
The correct answer is B. (5(x-3)(x+3)). First take (5) common and split \(x^2-9\) by difference of squares. Exam tip: look further after common factor.
Step 3
Exam Tip
पहले (5) समान निकालें और \(x^2-9\) को वर्गों के अंतर से तोड़ें। परीक्षा में समान गुणनखंड के बाद आगे देखें।
First take (x) common and factor \(x^2+3x+2\) as ((x+1)(x+2)). Exam tip: factor the trinomial after common factor.
Step 2
Why this answer is correct
The correct answer is B. (x(x+1)(x+2)). First take (x) common and factor \(x^2+3x+2\) as ((x+1)(x+2)). Exam tip: factor the trinomial after common factor.
Step 3
Exam Tip
पहले (x) समान निकालें और \(x^2+3x+2\) को ((x+1)(x+2)) करें। परीक्षा में सामान्य गुणनखंड के बाद त्रिपद भी तोड़ें।
